The overhead reach distances of adult females are normally distributed with a mean of 200 cm and a standard deviation of 8.3 cm. a. Find the probability that an individual distance is greater than 210.00 cm. b. Find the probability that the mean for 20 randomly selected distances is greater than 197.80 cm c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30?
Answer:
a) 0.1151 = 11.51% probability that an individual distance is greater than 210.00 cm.
b) 0.883 = 88.3% probability that the mean for 20 randomly selected distances is greater than 197.80 cm.
c) The distribution of the population is normal, which means that the sample size does not need to exceed 30.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
The overhead reach distances of adult females are normally distributed with a mean of 200 cm and a standard deviation of 8.3 cm.
This means that [tex]\mu = 200, \sigma = 8.3[/tex]
a. Find the probability that an individual distance is greater than 210.00 cm.
This is 1 subtracted by the pvalue of Z when X = 210. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{210 - 200}{8.3}[/tex]
[tex]Z = 1.2[/tex]
[tex]Z = 1.2[/tex] has a pvalue of 0.8849
1 - 0.8849 = 0.1151
0.1151 = 11.51% probability that an individual distance is greater than 210.00 cm.
b. Find the probability that the mean for 20 randomly selected distances is greater than 197.80 cm
Now [tex]n = 20, s = \frac{8.3}{\sqrt{20}} = 1.8559[/tex]
This probability is 1 subtracted by the pvalue of Z when X = 197.8. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{197.8 - 200}{1.8559}[/tex]
[tex]Z = -1.19[/tex]
[tex]Z = -1.19[/tex] has a pvalue of 0.117
1 - 0.117 = 0.883
0.883 = 88.3% probability that the mean for 20 randomly selected distances is greater than 197.80 cm.
c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30?
The distribution of the population is normal, which means that the sample size does not need to exceed 30.
I need some gosh darn help because I will fail my math test. Suppose two angles in a coordinate plane, one measuring 80 and the other measuring 160, were both rotated 180 about the origin and then translated 40 units down. which of these would be a measure of one of the resulting angles? Select 2 answers
Answer:
120 and 40
Step-by-step explanation:
Because when we subtract 80 and 40 is equal 40 or 160 and 40 is 120.
r+6<10 what’s the answer?
Answer:
r < 4
Step-by-step explanation:
r+6<10
r < 4
6t/9-22;t=60
please help me
Answer:
if t=60, then 6(60)/9-23. (360-198)/9
=18
1) Heather writes a number that shows 30 parts of 100. Select all that could be Heather's number. 0 0.30 3/100 30/10 0.3 30/100 ! This is a required question
Answer:
im guessing .30, .3, and 30/100
Step-by-step explanation:
im not sure how to explain it but fractions. yes.
s + 10.7 = 7.2
s = ?
how do i solve
Two sides of an obtuse triangle measure 12 inches and 14 inches. The longest side measures 14 inches
What is the greatest possible whole-number length of the unknown side?
Answer:
Step-by-step explanation:
If you add the lengths of two sides, 12 and 14, you will get 28. Using the above theorem, the third side cannot be greater than or equal to 28. Therefore, the greatest possible whole-number length of the unknown side is 27.
Answer:
Step-by-step explanation:
7 or C
Solve the system by substitution.
2x + 3y = 32
y = x + 9
Answer:
x=1 and y=10 (1,10)
Step-by-step explanation:
2+30=32
10=1+9
I will venmo if someone can please help me
Answer: 14.967
Step-by-step explanation:
Use Pythagorean Theorem to find the missing length.
a² + b² = c²
x² + 10² = 18²
x² + 100 = 324 [Subtract 100 from both side]
x²= 224
√x² = √224 [solve the square root from both sides]
x ≈ 14.967
please help helppppppp
C/2 - 3 + 6/d when c=14 d=3
Answer:
6
Step-by-step explanation:
14/2 - 3 + 6/3
Divide 14 by 2 to get 7.
7−3+6/3
Subtract 3 from 7 to get 4.
4+6/3
Divide 6 by 3 to get 2.
4+2
Add 4 and 2 to get 6.
6
PLEASE HELP THIS ASSIGNMENT IS OVER DUE
Answer:
91m + 13n + 52
Step-by-step explanation:
13(n + 4 + 7m)
= (13) (n+4+7m)
= (13) (n) + (13) (4) + (13) (7m)
= 13n + 52 + 91m
= 91m + 13n + 52
hope this helps and is right :)
p.s. i really need brainliest
Answer:
13n + 52 +91m
Step-by-step explanation:
As far as I can tell, all you are doing is distributing the 13 into the numbers. You multiply 13* 1n, 13*4, and 13*7m to give you 13n +52+91m.
A photographer has a print that is 3.5 inches wide and 2.5 inches tall. If the photographer enlarges the print so that it is 7 inches wide, how tall will it be?
5 inches
6 inches
8 inches
12 inches
Answer:
5 inches
Step-by-step explanation:
Hope I helped
Work out the size of angle x.
Answer:
First: 105
Second: 65
Third: 133
Fourth: 129
Fifth: 60
19. Frank and Jenny want to cut a plank for a sandbox they are making. If the plank is
12 inches long, and they want four pieces of equal size, how long will each piece measure?
A. 44 inches
44 in
B. 3 inches
C. 8 inches
0.3 inches
Answer:
it is 3 inches
3 x 4 = 12
What is the initial value of the equation shown? (1 point) y = −7x − 6 −13 −7 −6 −1
Answer:
-6
Step-by-step explanation:
The equation is y = -7x - 6.
The initial value is found when x = 0.
y = -7(0) - 6
y = 0 - 6
y = -6
The original cost is $25. The item has a discount of 20% off. What is the discount amount?
Answer:20 dollars.
not sure
Step-by-step explanation:
HELP PLEASE PLEASE HELP, also show work!
Answer:
1 6 3b 0ny 5i bhk
Step-by-step explanation:
All the prizes for the contest were won by Josh. Rewrite in an active voice.
Answer:
Josh won all the prizes for the contest
Step-by-step explanation:
Circumference = 69.1yd
Answer:
What do you want us to find?
Step-by-step explanation:
PLEASEEEE HELP THIS IS DUE TODAY!!!
Answer: $200
Step-by-step explanation:
On the X axis, it shows the kilograms. Since the problem asks for how much money she makes for 60 kg, go to the point on the X axis that represents 60 kg and then go up to the corresponding y or dollar value, which is 200.
Helpppppp please i need help on this question
Step-by-step explanation:
K=12 if you want explanation i will
Please answer <3 thanks
Answer:
The slope of the line would be 3/6 or 1/2
Step-by-step explanation:
To get from point (1,2) to point (7,5) you have to rise 3 places and run (move to the right) 6 times. Rise/run=3/6
hope this helps. ; )
Need answers for 1 and 2. Please
Answer:soultion
Step-by-step explanation: solution
Pls help this is due today! Find the value of x, then the value of each angle:
Answer:
x = 29
angles are 90 degrees, 56 degrees, and 34 degrees
Step-by-step explanation:
90 + (2X-2) + (X+5) = 180
3X + 93 = 180
3X = 87
X = 29
Please help I don't get this
Answer:
18n+9
Step-by-step explanation:
9(2n+1)
multiply the 9 with the numbers in the parenthesis18n+9
Which one of these grids is shaded red and blue in the ratio 0.5: 1?
A
B
D
E
F
Answer:
B
Step-by-step explanation:
Answer:
Its E
Step-by-step explanation:
Francine can ride 16 miles on her bicycle in 45 minutes. At this speed, how many minutes would it take Francine to ride 60 miles?
Answer:
2000 minutes on 16 miles
Answer:
168.75 minutes
Step-by-step explanation:
Francine's speed (the unit rate) is (16 miles) / (45 minutes), or 16/45 miles/min.
Recalling that distance = speed times time, we recognize that
time = distance / speed
which here is
(60 miles) / (16/45) miles/min = 168.75 minutes, or 168 min 45 sec
PLEASE ANSWER THIS QUESTION
Show that 4x – 7 is equivalent to 4(x - 1) – 3 when x = 3.
Answer:
4(3) - 7 = 4(3 - 1) - 3
12 - 7 = 4(2) - 3
5 = 8 - 3
= 5
They are equivalent because when they are both simplified they have the same answer 5
Dexter deposited 6,300 into a saving account that earns 2.60% simple interest per year. How much interest will she earn in 4 years
Answer:
2
Step-by-step explanation: