Answer:
a
The null hypothesis is [tex]H_o : \mu_1 - \mu_2 \le 0[/tex]
The alternative hypothesis is [tex]H_a : \mu_1 - \mu_2 > 0[/tex] (Manufacturers claim)
b
[tex]t = 2.114[/tex]
c
Decision rule
Reject the null hypothesis
d
There is sufficient evidence to support the claim that the calling range (in feet) of Manufacturers 900-MHz cordless telephone is greater than that of its leading competitor
Step-by-step explanation:
From the question we are told that
The first sample size is [tex]n_1 = 9[/tex]
The second sample size is [tex]n_2 = 12[/tex]
The first sample mean is [tex]\= x_1 = 1260 \ feet[/tex]
The second sample mean is [tex]\= x_2 = 1230[/tex]
The first standard deviation is [tex]\sigma_1 = 24[/tex]
The second standard deviation is [tex]\sigma_2 = 37[/tex]
The significance level is [tex]\alpha = 0.10[/tex]
The null hypothesis is [tex]H_o : \mu_1 - \mu_2 \le 0[/tex]
The alternative hypothesis is [tex]H_a : \mu_1 - \mu_2 > 0[/tex] (Manufacturers claim)
Generally the degree of freedom is mathematically represented as
[tex]df = n_1 + n_2 -2[/tex]
[tex]df = 9 + 12 - 2[/tex]
[tex]df = 19[/tex]
Generally the pooled standard deviation is mathematically represented as
[tex]\sigma_p = \sqrt{ \frac{(n_1 - 1)\sigma_1^2 + (n_2-1 )\sigma_2^2 }{ (n_1 - 1 ) + (n_2 - 1 )} }[/tex]
[tex]\sigma_p = \sqrt{ \frac{(9 - 1)24^2 + (12-1 )37^2 }{ (9 - 1 ) + (12 - 1 )} }[/tex]
[tex]\sigma_p =32.17[/tex]
Generally the test statistics is mathematically represented as
[tex]t = \frac{\= x_1 - \= x_2 }{\sqrt{\frac{\sigma_p^2}{n_1 } +\frac{\sigma_p^2}{n_2 } } }[/tex]
[tex]t = \frac{1260 - 1230 }{\sqrt{\frac{32.17^2}{9 } +\frac{32.17^2}{12 } } }[/tex]
[tex]t = 2.114[/tex]
Generally the p-value is obtained from the student t distribution table and the value is
[tex]p-value = P(t > 2.11) = t_{2.11 , 19} = 0.024173[/tex]
Given that the [tex]p-value < \alpha[/tex]
The null hypothesis is rejected
Hence we can conclude that there is sufficient evidence to support the claim that the calling range (in feet) of Manufacturers 900-MHz cordless telephone is greater than that of its leading competitor
What is 8 3/5 graphed on a number line
PLZ I NEED HELP ASAP CUZ IM ON A TIMER!
Answer:
Step-by-step explanation:
8 3/5 on a number line is between 8 and nine
idk how to draw a number line on a computer so ill just tell you how
1. divided the spaces between 8 and 9 into 5 sections ( 3/5 )
2. then mark 3 of those 5 spaces and put a dot or a line at where the 3rd space ends
Please help ill give brainlest
Answer & Step-by-step explanation:
For this problem, we have to find the equations that have a value of 10 for the variable y. Immediately, we can eliminate some answers. We can eliminate A, D, and E because they all have a different value for the variable y. So, that leaves us with answer choices B and C.
In order to check to see if we are correct, let's plug in 10 for the y in answer choices B and C.
B:
8 = 18 - y
8 = 18 - 10
8 = 8
C:
60 = 6y
60 = 6(10)
60 = 60
So, as you can see, we are correct and we have successfully found the correct answer to the given problem.
Answer:
B and C
Step-by-step explanation:
We want to find the equations where y=10 is a solution. Let's plug 10 into each equation and solve.
A. y+11=22
10 +11 =22
Add 10 and 11.
21 ≠ 22
21 does not equal 22. This choice is incorrect.
B. 8= 18-y
8=18-10
Subtract 10 from 18.
8=8
8 equals 8. This choice is correct.
C. 60=6y
60=6(10)
Multiply 6 and 10.
60=60
60 equals 60. This choice is correct.
D. y/5=4
10/5=4
Divide 10 by 5.
2≠4
2 does not equal 4. This choice is incorrect.
E. 10y=20
10(10)=20
Multiply 10 and 10.
100≠20
100 does not equal 20. This choice is incorrect.
The equations where y=10 is a solution are B. 8=18-y and C. 60=6y
What is 3,000 is 1/10 of
Answer:
30000
Step-by-step explanation:
3000 / (1/10) = w
3000*10/1 = w
30000 = w
probe:
30000*1/10 = 3000
then:
30000
is 1/10
of
30000
A box contains 12 balls: 8 red and 4 black. Two extractions are made without replacing the extracted ball to the box before the second extraction. Do you find the probability of drawing a ball of each color?
Answer:
16/33
Step-by-step explanation:
The probability that the first ball is red and the second ball is black is:
8/12 × 4/11 = 8/33
The probability that the first ball is black and the second ball is red is:
4/12 × 8/11 = 8/33
So the total probability of drawing one ball of each color is 8/33 + 8/33 = 16/33.
Let y = (2 6) and u = (7 1). Write y as the sum of a vector in Span(u) and a vector orthogonal to .
The question is missing. Here is the complete question.
Let y = [tex]\left[\begin{array}{ccc}2\\6\end{array}\right][/tex] and u = [tex]\left[\begin{array}{ccc}7\\1\end{array}\right][/tex]. Write y as the sum of a vector in Span(u) and a vector orthogonal to u.
Answer: y = [tex]\left[\begin{array}{ccc}\frac{21}{10} \\ \frac{3}{10} \end{array}\right] + \left[\begin{array}{ccc}\frac{-1}{10}\\ \frac{57}{10} \end{array}\right][/tex]
Step-by-step explanation: The sum of vectors is given by
y = [tex]y_{1}[/tex] + z
where [tex]y_{1}[/tex] is in Span(u);
vector z is orthogonal to it;
First you have to compute the orthogonal projection [tex]y_{1}[/tex] of y:
[tex]y_{1}[/tex] = proj y = [tex]\frac{y.u}{u.u}.u[/tex]
Calculating orthogonal projection:
[tex]\left[\begin{array}{c}2\\6\end{array}\right][/tex].[tex]\left[\begin{array}{c}7\\1\end{array}\right][/tex] = [tex]\left[\begin{array}{c}9\\6\end{array}\right][/tex]
[tex]\left[\begin{array}{c}7\\1\end{array}\right][/tex].[tex]\left[\begin{array}{c}7\\1\end{array}\right][/tex] = [tex]\left[\begin{array}{c}49\\1\end{array}\right][/tex]
[tex]y_{1} = \frac{9+6}{49+1}.u[/tex]
[tex]y_{1} = \frac{15}{50}.u[/tex]
[tex]y_{1} = \frac{3}{10}.u[/tex]
[tex]y_{1} = \frac{3}{10}.\left[\begin{array}{c}7\\1\end{array}\right][/tex]
[tex]y_{1} = \left[\begin{array}{c}\frac{21}{10} \\\frac{3}{10} \end{array}\right][/tex]
Calculating vector z:
z = y - [tex]y_{1}[/tex]
z = [tex]\left[\begin{array}{c}2\\6\end{array}\right] - \left[\begin{array}{c}\frac{21}{10} \\\frac{3}{10} \end{array}\right][/tex]
z = [tex]\left[\begin{array}{c}\frac{-1}{10} \\\frac{57}{10} \end{array}\right][/tex]
Writing y as the sum:
[tex]y = \left[\begin{array}{c}\frac{21}{10} \\\frac{3}{10} \end{array}\right] + \left[\begin{array}{c}\frac{-1}{10} \\\frac{57}{10} \end{array}\right][/tex]
Using the number 98,045,132.706
(a) The digit 8 is in the
place.
(b) The digit 3 is in the
place.
Answer:
A. The digit 8 is in the place one million position
B. The digit 3 is in the place tens position
Step-by-step explanation:
Given:
98,045,132.706
9 is in the ten million position
8 is in the one million position
0 is in the hundred-thousand position
4 is in the ten-thousand position
5 is in the one-thousand position
1 is in the hundred position
3 is in the tens position
2 is in the one position
. Decimal
7 is in the tenth position
0 is in the hundredth position
6 is in the thousandth position
Therefore,
A. The digit 8 is in the place one million position
B. The digit 3 is in the place tens position
If lim f (x) x →5 = 2 and lim g (x) x → 5= -6 which of these limits exist?
Answer:
E
Step-by-step explanation:
So we already know that:
[tex]\lim_{x \to 5} f(x)=2 \text{ and } \lim_{x \to 5} g(x)=-6[/tex]
So, go through each of the choices and see which ones are correct.
I)
We have:
[tex]\lim_{x \to 5} (f(x)+g(x))[/tex]
This is the same as saying:
[tex]\lim_{x \to 5} f(x)+ \lim_{x \to 5} g(x)[/tex]
And since we already know the values:
[tex]=(2)+(-6)\\=-4[/tex]
So, the limit does indeed exist.
II)
We have:
[tex]\lim_{x \to 5} \frac{f(x)}{g(x)+6}[/tex]
This is the same as:
[tex]\frac{ \lim_{x \to 5} f(x)}{ \lim_{x \to 5} g(x)+ \lim_{x \to 5} 6 }[/tex]
The bottom right one is just 6. Simplify:
[tex]\frac{ \lim_{x \to 5} f(x)}{ \lim_{x \to 5} g(x)+6}[/tex]
Substitute the values we know:
[tex]=\frac{(2)}{(-6)+6} \\=2/0[/tex]
This is a value over zero. Unlike the indeterminate form 0/0, this limit does not exist.
III)
We have:
[tex]\lim_{x \to 5} \frac{f(x)-2}{g(x)}[/tex]
Again, this is the same as:
[tex]\frac{ (\lim_{x \to 5} f(x))-2}{ \lim_{x \to 5} g(x)}[/tex]
Substitute in the values we know:
[tex]=\frac{(2)-2}{(-6)}\\ =0/-6=0[/tex]
The limit does exist and it is 0.
So, the limits of only I and III exist.
The correct answer is E.
Someone, please help me with this.
Answer:
14
Step-by-step explanation:
7x-1+6x-1=180
13x-2=180
13x=180+2
13x=182
x=14
Suppose a horticulturist measures the aboveground height growth rate of four different ornamental shrub species grown in a greenhouse. The shrubs were grown from a random sample of seeds, and they were all grown in the same soil mixture and in the same size pot. To ensure that any slight differences in the environmental conditions throughout the greenhouse are not confounded with species, she randomizes the location of the pots throughout the greenhouse. The table contains a summary of her data. Population Sample Sample Sample Population description size standard deviation 17.153 cm/year 2.666 cm/year x2 = 13.983 cm/year s2-3.605 cm/year 15.120 cm/year3 3.774 cm/year x4-14.328 cm/year s.-3.011cm/year mean 1 Species 1 n1-20 Species 2 n2=20 3 Species 3 n 20 Species 4 n4-20 The growth rate distributions of each sample are approximately normal, and the data do not contain outliers. The horticulturist uses a one-way analysis of variance (ANOVA) at a significance level of a 0.05 to test if the mean growth rates of all four species are equal. Her results are shown in the table. Source of variation Between groups Within groups Total ss MS p-valuef-critical 120.988 3 40.329 3.7160.0152.725 824.710 76 10851 945.697 79Complete the sentence to state the decision and conclusion of horticulturist test.The decision is to ________the ___________at a significant level of________ α=0.05 There is _______ evidence to conclude that __________ is__________.
Complete Question
The complete question is shown on the first uploaded image
Answer:
The decision is to reject the null hypothesis at a significant level of significance [tex]\alpha = 0.05[/tex] There is sufficient evidence to conclude that at least one of the population mean is different from at least of the population
Step-by-step explanation:
From the question we are told that the claim is
The mean growth rates of all four species are equal.
The null hypothesis is
[tex]H_o : \mu _1 = \mu_2 = \mu_3 = \mu_4[/tex]
Th alternative hypothesis is
[tex]H_a: at \ least \ one \ of \ the \ means \ is \not\ equal[/tex]
From question the p-value is [tex]p-value = 0.015[/tex]
And since the [tex]p-value < \alpha[/tex] so the null hypothesis will be rejected
So
The decision is to reject the null hypothesis at a significant level of significance [tex]\alpha = 0.05[/tex] There is sufficient evidence to conclude that at least one of the population mean is different from at least of the population
Which number produces ab irrational number when multipled by 4
Answer:
Step-by-step explanation:
Hello, any irrational number multiplied by 4 is an irrational number.
For instance, you can take
[tex]\boxed{\sqrt{2}}[/tex]
Thank you
A 92-ft tree casts a shadow that is 120 ft long. What is the angle of elevation of the sun?
Answer:
The angle of elevation of the sun is 38°
Step-by-step explanation:
We can set up the diagram for the the question by interpreting it, you can check the diagram at the attached file.
We can see that after the interpretation of the question we arrived at a triangle,. Where the vertical side represent the 92-ft. which is the height of the tree and the horizontal side represent the 120 ft. which is the shadow's lenght. Then the angle of elevation of the sun can ba calculated using tangent ratio, from our knowledge of trigonometry
Tan(θ )= opposite/adjacent
Where our opposite =92ft
Adjacent= 120ft
Tan(θ ) =92/120
θ =tan-1( 92/120)
θ = 37.48°
Therefore, the angle of elevation of the sun If we round up our decimal value to the nearest 10th, we have θ = 38°
Keith has 39 books in his library. He bought several books at a yard sale over the weekend. He now has 84 books in his library. How many books did he buy at the yard sale ?
Answer:
total books in library = 39
books bought from yard sale = ??
Total book in library now = 84
Now,
books bought from yard sale= 39-84
= 45
Is the a discrete random variable, a continuous random variable, or not a random variable? response to the survey question "Did you smoke in the last week?" A. It is a discrete random variable. B. It is a continuous random variable. C. It is not a random variable.
Answer:
The correct answer is:
It is a discrete random variable. (A)
Step-by-step explanation:
Discrete Random Variables are variables that have distinct values. The number of variables that can be taken on can be counted. in this example, the variables to the question Did you smoke in the last week? is one of two possibilities; yes or no. Apart from these two values, there is no other possibility for the variables, hence it is a discrete random variable
Continuous Random Variables are values that can take on any value between distinct values, even up to infinity. The number of values that the variables can take on cannot be counted or listed. For example, is there are variables for the possible temperature that a particular city can take on in a day, the values are continuous random variables because the values do not have any distinct value, and the possibilities cannot be counted. the possibilities can be; anywhere between 20°C to 50°C. between these two, temperatures, you can have infinite possibilities; 20.1, 30.5, 40.8, etc. Hence the values cannot be counted, it is thus a continuous random variable.
Answer:
c not random variable
Step-by-step explanation:
Use the value of the linear correlation coefficient to calculate the coefficient of determination. What does this tell you about the explained variation of the data about the regression line? About the unexplained variation?
r=0.864
a) Calculate the coefficient of determination.
(Round to three decimal places as needed.)
b) What does this tell you about the explained variation of the data about the regression line?
c) What % of the variation can be explained by the regression line.
(Round to one decimal place as needed.)
About the unexplained variation?
d) What % of the variation is unexplained and is due to other factors or to sampling error.
(Round to one decimal place as needed.)
Answer:
Kindly check explanation
Step-by-step explanation:
Given the Coefficient of correlation (r) = 0.864
The Coefficient of determination (R^2) :
0.864^2 = 0.747 ( 3 decimal places)
B) the Coefficient of determinationR^2 tells about the proportion of variation in the dependent variable that is predicted by the independent variable, Hence, a proportion of about 0.75 should fall within the regression line.
C) percentage variation explained :
Coefficient of determination * 100%
0.747 * 100% = 74.7%
D) unexplained variation due to other factors or sampling error :
(total variation - explained variation) = (100 - 74.7)% = 25.3%
simplify 3×+1(2×-1)2-1(6×)
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hi my lil bunny!
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
Answer = [tex]\boxed {x - 2}[/tex]
[tex]3x +1(2x-1)2-1(6x)[/tex]
= [tex]\boxed {3x + 1 . ( 2x - 1 ) . 2 - 1 (6x) = x - 2}[/tex]
Steps :
[tex]3x + 1 . (2x - 1) . 2 - 1 . (6x)[/tex]
Remove the parentheses : [tex](a) = a[/tex]
[tex]= 3x + 1 * (2x- 1) * 2 - 1 * 6x[/tex]
Multiply the numbers : [tex]1 * 2 = 2[/tex]
[tex]= 3x + 2 ( 2x - 1 ) * 6x[/tex]
Multiply the numbers : [tex]1 * 6 = 6[/tex]
[tex]= 3x + 2 ( 2x - 1 ) -6x[/tex]
Expand: [tex]2 (2x - 1) : 4x - 2[/tex]
[tex]2 ( 2x - 1 )[/tex]
Apply the distributive law : [tex]a (b - c) = ab - ac[/tex]
[tex]a = 2, b = 2x, c = 1 \\= 2 * 2x - 2 * 1[/tex]
Simplify [tex]2 * 2x - 2 * 1 : 4x - 2[/tex]
= [tex]= 4x - 2[/tex]
[tex]= 3x + 4x - 2 - 6x[/tex]
Simplify [tex]3x + 4x - 2 - 6x : x - 2[/tex]
= [tex]x - 2[/tex]
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Have a great day/night!
❀*May*❀
Y=x-1 4x+8=y solve the system
how many terms are in the exspression 4{8+3x]
2 terms
Step-by-step explanation:
4[8+2x]
=4*8+4*2x
=32+8x
therefore there are 2 terms
hope it helps u if yes pls mark brainliest
Answer:
The first factor (4) consists of one (1) term, "4".
The second factor (8 +3x) consists of two (2) terms, "8" and "3x".
graph the inequality 7< y -3x < 11
Answer:
X=5 Y=-4
Step-by-step explanation:
If 4x— 3 = 2x + 9, then x = ?
x=6
x=2
x=1
x=3
Answer:
x=6 is the answer
Step-by-step explanation:
4x-3=2x+9
adding 3 on both sides
4x-3+3=2x+9+3
4x=2x+12
subtracting 2x on both sides
4x-2x=2x-2x+12
2x=12
dividing 2 on both sides
2x/2=12/2
x=6 is the answer.
hope it will help you :)
Step-by-step explanation:
4x - 3 = 2x + 9
Bringing like terms on one side
4x - 2x = 9 + 3
2x = 12
x = 12/ 2
x = 6
metric conversions, which is bigger
Answer: 6 m is greater
Step-by-step explanation:
Cm is less than m
Hope it helps
Answer:
25. <
26. <
27. >
28. <
29. <
30. >
Hope it helps!
lovelymoonlight ✨
please help me /:
Given the table of values below, which of the following ordered pairs are
found on the graph of the inverse function?
Answer:
see below
Step-by-step explanation:
The ordered pairs of the inverse function are the reverse of the ordered pairs of the function.
You are given the function has ordered pairs (-3, -2), (3, -1) and so on. The inverse function will have ordered pairs (-2, -3), (-1, 3), and so on. This matches choice A.
what is the greatest common factor of 60 , 8
Answer:
4
Step-by-step explanation:
The factors of 8 are 1, 2, 4, and 8.
60 is not divisible by 8, but it is divisible by 4: 4 * 15 = 60. So the GCF of 60 and 8 is 4.
000KS
c. Sumana runs a tea shop and she buys 7.5L of milk everyday. If she
uses 4.75L of milk in the morning and the remaining milk in the
evening. Find the quantity of milk she uses in the evening
Answer:
2.75 L
Step-by-step explanation:
This is the problem of subtraction.
Total Milk sumana has = 7.5 l
Milk used in the morning = 4.75 L
Milk left for evening = Total Milk sumana has - Milk used in the morning
Milk left for evening = 7.5 l - 4.75 l = 2.75 L
What is the value of y in the equation 6.4x + 2.8y = 44.4, when x = 3?
Answer:
y = 9
Step-by-step explanation:
So if x = 3, we can sub that into the equation.
This gives us:
6.4 (* 3) + 2.8y = 44.4
so:
19.2 + 2.8y = 44.4
25.2 = 2.8y
so
y = 9
Answer: 9
Step-by-step explanation: plug 3 into the x, then use the order of operations/ pemdas to solve. first multiply 6.4 and 3 (=19.2) then subtract the answer from 44.4 (now the equation is 2.8y=25.2) then divide 2.8 from 25.2 to get x alone and you are left with x=9
An accident investigator measured the skid marks of one of the vehicles involved in an accident. The length of the skid marks, d, was 117ft. Use the formula s=24d−−−√ to find s, the speed of the vehicle before the brakes were applied. Round your answer to the nearest tenth.
Answer:
The speed is 2808 ft/sStep-by-step explanation:
step one:
In this problem we are expected to substitute the value of d in the expression for velocity given as
[tex]s=24d[/tex]
step two:
Given that
d= 117 ft
Substituting the value for d in the given equation we have
[tex]s= 24*117\\\\s=2808 ft/s[/tex]
The problem basically tests our ability to perform basic substitution operation which we have performed, should you have any question or doubt, kindly respond to this question
Answer:
53
Step-by-step explanation:
7 1/8 + 1/6, reduced to lowest terms
Answer:
Step-by-step explanation:
7 3/24 + 4/24
7 7/24
Simplify the expression:
(10x2 -1 + 4x) + (3 + 5x2 - 4x)
Answer:
[tex] \boxed{\sf 15x^2 + 2} [/tex]
Step-by-step explanation:
Simplify the expression:
[tex] \sf \implies(10 {x}^{2} - 1 + 4x) + (3 + 5 {x}^{2} - 4x)[/tex]
Grouping like terms, 10x² + 5x² + 4 x - 4 x - 1 + 3 = (10 x² + 5x²) + (4 x - 4 x) + (-1 + 3):
[tex] \sf \implies (10 x^2 + 5 x^2) + (4 x - 4 x) + (-1 + 3)[/tex]
10x² + 5x² = 15x²:
[tex] \sf \implies 15 x^2 + (4 x - 4 x) + (-1 + 3)[/tex]
3 - 1 = 2:
[tex] \sf \implies 15 x^2 + (4 x - 4 x) + 2[/tex]
4 x - 4 x = 0:
[tex] \sf \implies 15 x^2 + 2[/tex]
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
Answer:
change f(x) to y, switch x and y, and solve for y
y = √(x -4)
x = √(y - 4)
x² = y - 4
x² + 4 = y
y = x² + 4
f⁽⁻¹⁾ = x² + 4, where x ≥ 4
How to solve this brainteaser
Answer:
last row equals 333
Step-by-step explanation:
The clock showing time 9:00 should be worth 9 points, and the clock showing 3:00 should be worth 3 points, giving for the first row:
9 + 9 + 3 = 21
the three equal calculators showing 1234 are worth 10 points each:
1+2+3+4 = 10
and 10 + 10 + 10 = 30
the light bulbs should be 15 points each then giving 15 + 15 - 15 = 130 - 15 = 15 Notice also that they all have 5 rays of light coming out (so a 3 points per ray)
Now for the bottom line we have:
9 + (1+2+2+4) times 3 * 12 (only four rays on each bulb thus 4 * 3 = 12)
Notice we added the figures that appear in the calculator.
9 + 9 * 36 = 333
For a confidence level of 85%, find the critical value for a normally distributed variable. The sample mean is normally distributed if the population standard deviation is known.
Answer:
The value is [tex]Z_{\alpha } = 1.439[/tex]
Step-by-step explanation:
From the question we are told that
The confidence level is C = 85%
Generally the level of significance is mathematically represented as
[tex]\alpha = (100 - 85 )\%[/tex]
[tex]\alpha = 0.15[/tex]
Now from the normal distribution table the critical value of [tex]\alpha[/tex] is
[tex]Z_{\alpha } = 1.439[/tex]