Suppose the weights of apples are normally distributed with a mean of 85 grams and a standard deviation of 8 grams. The weights of oranges are also normally distributed with a mean of 131 grams and a standard deviation of 20 grams. Amy has an apple that weighs 90 grams and an orange that weighs 155 grams.

Required:
a. Find the probability a randomly chosen apple exceeds 100 g in weight.
b. What weight do 80% of the apples exceed?

Answers

Answer 1

Answer:

a) 0.0304 = 3.04% probability a randomly chosen apple exceeds 100 g in weight.

b) The weight that 80% of the apples exceed is of 78.28g.

Step-by-step explanation:

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 z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Weights of apples are normally distributed with a mean of 85 grams and a standard deviation of 8 grams.

This means that [tex]\mu = 85, \sigma = 8[/tex]

a. Find the probability a randomly chosen apple exceeds 100 g in weight.

This is 1 subtracted by the p-value of Z when X = 100. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{100 - 85}{8}[/tex]

[tex]Z = 1.875[/tex]

[tex]Z = 1.875[/tex] has a p-value of 0.9697

1 - 0.9696 = 0.0304

0.0304 = 3.04% probability a randomly chosen apple exceeds 100 g in weight.

b. What weight do 80% of the apples exceed?

This is the 100 - 80 = 20th percentile, which is X when Z has a p-value of 0.2, so X when Z = -0.84.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-0.84 = \frac{X- 85}{8}[/tex]

[tex]X - 85 = -0.84*8[/tex]

[tex]X = 78.28[/tex]

The weight that 80% of the apples exceed is of 78.28g.


Related Questions

Find the volume of the cone

Answers

Volume= 37. 7

V=π r² h/3 = π · 22 · 9/3 ≈37.69911

I hope this helps!

how many oranges and mangoes are in the basket altogether if the ratio of mangoes and oranges in the basket is 2/5if there are 40 oranges in the basket ​

Answers

9514 1404 393

Answer:

  56

Step-by-step explanation:

We are given ...

  mangoes : oranges = 2 : 5

Then the ratio we want is ...

  (mangoes +oranges) : oranges = (2 +5) : 5 = 7 : 5

The total number of fruits in the basket is ...

  (7/5)(40) = 56 . . . mangoes + oranges in the basket

Name the
alternate
interior angle
with angle 5.
HELPP PLEASEEE

Answers

Answer:

angle 4 isthe correct answer

Sonia took a loan of $10 000 from ABC bank tob pay for a renovation at home. The bank offered her a period of 30 months at a rate of 10.5%. to repay the loan:

a) Calculate the Simple Interest she would pay in 30 months.

b) Calculate the Total amount Sonia would have to repay the bank.

Answers

Answer:

a. Simple interest, S.I = $2,625

b. Total amount = $12,625

Step-by-step explanation:

Given the following data;

Principal = $10,000

Interest rate = 10.5%

Time = 30 months to years = 2.5 years

a. To find the simple interest;

Mathematically, simple interest is calculated using this formula;

[tex] S.I = \frac {PRT}{100} [/tex]

Where;

S.I is simple interest. P is the principal. R is the interest rate. T is the time.

Substituting into the formula, we have;

[tex] S.I = \frac {10000*10.5*2.5}{100} [/tex]

[tex] S.I = \frac {262500}{100} [/tex]

Simple interest, S.I = $2,625

b. To calculate the total amount Sonia would have to repay the bank;

Total amount = simple interest + principal

Total amount = 2625 + 10000

Total amount = $12,625

A man is changing the oil in his car. The instruction manual indicates that the car hold pints of oil. The man only has a cup measure. How many cups equal three pints?

Answers

The volume contained in a cup of oil is a fraction of the volume

contained in a pint of oil.

Correct response:

6 cups

Method used for the above unit conversion

The measure of the volume of oil the car holds = Pints of oil

The measurement the man has for use = Cups of oil

Required:

The number of cups equal to three pints.

Solution;

1 pint of oil = 2 cups of oil

Therefore;

3 pints of oil = 3 × 2 cups of oil = 6 cups of oil

The number of cups of oil equal to 3 pints of oil is 6 cups of oil

Learn more about units conversion here:

https://brainly.com/question/4845674

What is the common denominator of

Please ignore my choice I had to click one of them

Answers

Answer:

Your choice is correct. GOOD JOB!!

Step-by-step explanation:

1. Round 0.007492 to the nearest hundredth.

Answers

Answer:

The answer is 0.01

Step-by-step explanation:

so in order to round it you have to know after the decimal it goes: tenths, hundreds, thousands (0 tenths, 0 hundreds, 0 thousands)

So 0.007492, take the first 3 numbers after the decimal, 0.007, since it will be in the hundreds place, lets see if we can round the 0 up. If the number behind 0 is greater then or equal to 5 round up, if the number is less then 5 then it stays the same. Since 7>5 it rounds up, so the 0 becomes 1. So your new number will be 0.01

Hoped this helped :D

By rounding 0.007492 to the nearest hundredth, we get 0.01.

What is the method of rounding a number?

The number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.

Example: 0.3879 rounded to the nearest hundredth is 0.39.

If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down.

Example: 0.3823 rounded to the nearest hundredth is 0.38.

Given number is 0.007492.

Rounding to nearest hundredth, we get:

0.00749 ⇒ 0.01.

Learn more about rounding a number to nearest hundredth here: https://brainly.com/question/13313945

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Twice a number added to another number is –8. The difference of the two numbers is 2. Find
the numbers​

Answers

Answer:

-2 and -4

Step-by-step explanation:

→ Make variable's for each number

x is the first variable and y is the second

→ Form equations

2x + y = -8

x - y = 2

→ Solve

3x = -6

→ Divide both sides by 3

x = -2

→ Resubstitute that into one of the equations

-2 - y = 2

→ Add 2 on both sides

-y = 4 therefore y = -4

Please someone simplify this and please show the workout

Answers

Step-by-step explanation:

(a) 3pq / 4r² × 2rs / 6q²......first start by expanding the expression

It will be ;

3 × p × q / 4 × r × r X 2 × r × s / 6 × q × q

so now ,cancel out like terms. The q on top can cancel out with the q down same thing happens to r

so you'll get something like ;

3 × q / 4 × r X 2 × s / 6 × q ......so now divide , like 3 into 6 and 2 into 4 ,then you'll get something like;

qs / 4q

that's the answer

(b)15 ab² / 8 c²d ÷ 3ab / 4cd.......start by changing the sign from ÷ to × and then 3ab and 4cd will switch places

15ab² / 8c² d × 4cd / 3ab.....expand the expression

15 ×a×b×b / 8×c×c×d X 4×c×d / 3×a×b

then cancel like terms and you'll get;

15b / 8c X 4/3.....then divide 3 into 15 and 4 into 8

5b / 2c

hope this helps

A positive real number is 5 more than another. When - 10 times the smaller is added to the square of the larger, the result is 57. Find the numbers.

Answers

Answer:

4√2 and 5+4√2

Step-by-step explanation:

Let the two numbers be x ad y

Smaller = y

Bigger = x

If a positive real number is 5 more than another, then;

x = 5 + y ... 1

When - 10 times the smaller is added to the square of the larger, the result is 57, then;

-10y + x² = 57 ...2

Substitute 1 into 2;

-10y + (5+y)² = 57

-10y + 25+10y+y² = 57  

y²+25 = 57

y² = 57 - 25

y² = 32

y = √32

y = 4√2

Since x = 5 + y

x = 5 + 4√2

Hence rhe numbers are 4√2 and 5+4√2

The Hernandez family is evenly splitting 777 liters of gasoline between their 444 cars.
How many liters of gasoline should each car get?

Answers

Answer:

1.75 liters per car

Step-by-step explanation:

777liters /444 cars=1.75 liters per car

Solve for x.Round to the nearest tenth of a degree, if necessary. MKL,14,7.4

Answers

Answer:

m(∠LMK) = 27.9°

Step-by-step explanation:

We have to calculate the measure of angle LMK.

Measure of opposite side (KL) = 7.4

Measure of adjacent side (ML) = 14

By applying tangent rule in the given triangle,

tan(∠LMK) = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]

                 = [tex]\frac{KL}{ML}[/tex]

                 = [tex]\frac{7.4}{14}[/tex]

                 = 0.52857

m(∠LMK) = [tex]\text{tan}^{-1}(0.52857)[/tex]

               = 27.9°

Please help me with this problem

Answers

Answer:

x = 19

Step-by-step explanation:

2x + 3 = 90 - 49

2x + 3 = 41

2x = 38

x = 19

You recently invested $400,000 of your savings in a security issued by a large company. The security agreement pays you 12% per year and has a maturity of five year from the day you purchased it. What is the total cash flow you expect to receive from this investment, if compounded quarterly, separated into the return on your investment?

Answers

Answer:

$722444.49386776

Step-by-step explanation:

Use Compound Intrest Formula

[tex]a = p(1 + \frac{r}{n} ) {}^{nt} [/tex]

where p is the original amount.R is the amount of percentage compoundedN is amount of times compounded per year.T is how long the interest last.

P is 400,00p

T is 12% or 0.12

N is 4 since it is compounded quarterly

T is 5.

Plug the values in

[tex]400000(1 + \frac{0.12}{4} ) {}^{20} [/tex]

Ypu get

$722444.49386776

Consider the terms pyramid, line, square, and triangle. The term
is not defined in Euclidean geometry.

Answers

The term line is not defined in Euclidean geometry. ... These words are point, plane and line and are referred to as the "three undefined terms of geometry".

Answer:

LINE is not defined by Euclidian geometry

Step-by-step explanation:

In Euclidean geometry, there are 3 terms that are considered "undefined" they are; point, line and plane.  I think it is because considered undefined because they are described, but not every formally defined.

As in a shape I mean I hope I am right,

What percentage of total hours was spent playing football

Answers

Answer:  20

Explanation:

10 hours was spent playing football, out of 50 total

10/50 = 1/5 = 0.20 = 20%

A sequence is defined by the recursive function f(n + 1) = f(n). It f(3) = 9, what is f{1) ?

Answers

Answer:

because f(n) = f(n + 1)

=> f(3) = f(2) = f(1) = 9

What are the zeros of P(m) = (m2 – 4)(m2 + 1)?

Answers

Answer:

m=4, -1

Step-by-step explanation:

if i am interpreting this correctly, you are wanting to find at what value of m would the solution be zero.

so, there are two expressions that can cause an answer of 0.

1) if 0=m2-4

so solve for m2, and you get 4=m2

2) if 0=m2+1

solve for m2, and you get -1=m2

you can check your work by plugging the values back into the equation.

P(m)=(4-4)(4+1)

=(0)(5)

=0

and

P(m)=(-1-4)(-1+1)

=(5)(0)

=0

please solve in the next 10 minutes pleaseeee

Answers

Answer:

43.82 mph

266.67 feet

Step-by-step explanation:

Given :

S = √30fl

S = speed of car

f = drag Coefficient

l = Length of skid mark

If f = 0.8 ; l = 80 feets

s = √30fl

s = √(30*0.8*80)

s = √1920

s = 43.817

s = 43.82 mph

B.)

s = 80 mph

f = 0.8

s = √30fl

80 = √30*0.8*l

80 = √24l

Square both sides

80² = 24l

6400 = 24l

l = 6400/24

l = 266.67 feets

help pls i'll mark brainliest.. state the length of the line segment shown.

Answers

Answer:

i believe its 3 but i could be wrong

Step-by-step explanation:

sorry if i am..

3 because you can literally count, they even have grids and everything


In order for the data in the table to represent a linear
function with a rate of change of +5, what must be the
value of a?

Answers

Answer:

Step-by-step explanation:

Answer: C) a=18

Step-by-step explanation: Hope i helped :)

Which rational functions have an oblique asymptote? Check all that apply.
x2 + 1
(x) =
X
o
f(x) =
4x2 - 6
x + 1
O
f(x) =
*5
f(x) =
x3 + 1
x3 +2
f(x) =
x² + 3x

Answers

Answer:

A, B, E

Step-by-step explanation:

In the list of rational functions, 1st, 2nd, 4th, and 5th are the rational functions those have an oblique asymptote.

What is a function?

"A function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function."

The given rational functions are:

1. [tex]f(x) = \frac{x^{2}+1}{x}[/tex]

As the degree of numerator(2) is greater than the degree of denominator(1), This function has an oblique asymptote.

2. [tex]f(x) = \frac{4x^{2}-6}{x+1}[/tex]

As the degree of numerator(2) is greater than the degree of denominator(1), This function has an oblique asymptote.

3. [tex]f(x) = \frac{-x}{x^{2} }[/tex]

As the degree of numerator(1) is less than the degree of denominator(2), This function does not have an oblique asymptote.

4. [tex]f(x) = \frac{x^{5}}{x^{3}+1}[/tex]

As the degree of numerator(5) is greater than the degree of denominator(3), This function has an oblique asymptote.

5. [tex]f(x)= \frac{x^{3}+2}{x^{2}+3x}[/tex]

As the degree of numerator(3) is greater than the highest degree of denominator(2), This function has an oblique asymptote.

Learn more about a function here: https://brainly.com/question/15642520

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Mr watson rives 82 miles round trip each day how many miles does mr waton travel in 23 dys?

Answers

Answer:

1886 miles

Step-by-step explanation:

82 x 23 is 1886, 82 miles each day times 23 days.

If paper was £1.99 a pack and is now £3.98 a pack, what is the percentage increase in the price of the product?

Answers

Answer:

100%

Step-by-step explanation:

The initial price of the paper = 1.99

The final price of the pack of paper = 3.98

We need to find the percentage increase in the price of the product. It can be solved as follows :

[tex]\%=\dfrac{3.98-1.99}{1.99}\times 100\\\\=100\%[/tex]

So, the percentage increase in the price of the product is 100%.

please help with the steps thx:)

Answers

Answer:

The answer for the first is $350,325.378, I think

Step-by-step explanation:

I hope this helps, if im wrong im sorry

Answer:

interest: 945,  FV: 6345

FV= 323711.4, Interest: 226211.4

25.21 years

Step-by-step explanation:

question 1:

simple interest formula

PV(1+it)

30 months is equal to 30/12 years or 2.5 (so t= 2.5)

5400(1+.07*2.5)= 6345

This is the future value, to find the interst subtract the present value

6345-5400= 945

2.)

future value of continously compounding interst:

PV(e^(it))

97500*e^(.06*20)= 323711.4

finding the interest is the same as the last one

323711.4-97500=226211.4

3.)

same formula

let x= time in years

[tex]30000=7500e^{.055x}\\4=e^{.055x}\\\ln(4)=.055x\\x=25.20535202[/tex]

i guess we can round this to 25.21

Which of the following represents a function?

Answers

C I think (sorry if I’m wrong)

HELP ME PLEASE!!!
GIVEN sin0= √23/12
tan0= √23/11
Find cos0

Answers

Answer:

[tex]cos \theta = \frac{11}{12}[/tex]

Step-by-step explanation:

[tex]sin \theta = \frac{\sqrt{23}}{12} \ , \ tan \theta = \frac{\sqrt{23}}{11}\\\\tan \theta = \frac{sin \theta }{cos \theta }\\\\ \frac{\sqrt{23}}{11} = \frac{\frac{\sqrt{23}}{12} }{cos \theta}\\\\cos \theta = \frac{\frac{\sqrt{23}}{12} }{\frac{\sqrt{23}}{11} }\\\\cos \theta = \frac{\sqrt{23}}{12 } \times \frac{11}{\sqrt{23}}\\\\cos \theta = \frac{11}{12}[/tex]

Find the Surface Area and the Volume.

Answers

Answer:

volume = 1,000

surface area = 930

Step-by-step explanation:

the volume = (½×(14+6) ×4) × 25

= 1,000 cm³

the surface area =

(2×½×(14+6) ×4) + ((14+7+7+6) ×25)

= 80+850

= 930 cm²

A researcher has obtained the number of hours worked per week during the summer for a sample of 15 students. 40 25 35 30 20 40 30 20 40 10 30 20 10 5 20 Using this data set, compute the following: a. Median b. Mean c. Mode d. 40th percentile e. Range f. Sample variance g. Standard deviation

Answers

Answer:

Mean = 25

Median = 25

Mode = 6

Step-by-step explanation:

Given the data :

Using calculator :

Mode = highest occurring data point

Range = max - min = 40 - 5 = 35

Sample variance = 128.57 (calculator)

Sample standard deviation = sqrt(variance) = 11.34

A bill originally amounting Rs 1550, now amounts to Rs 1736 after adding VAT. Find the VAT rate.kaabil original amounting ​

Answers

Answer: 12%

Step-by-step explanation:

Original amount = Rs 1550

VAT = Rs 1736 - Rs 1550 = Rs 186

VAT rate = VAT/Original amount × 100

= 186/1550 × 100

= 18600/1550

= 12%

Therefore, the VAT rate is 12%.

Check:

= Rs 1550 + (12% × Rs 1550)

= Rs 1550 + $186

= Rs 1736

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