1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Ludmilka [50]
2 years ago
10

Slices of pizza for a certain brand of pizza have a mass that is approximately normally distributed with a mean of 67.7 grams an

d a standard deviation of 2.28 grams. Round answers to three decimal places. a) For samples of size 20 pizza slices, what is the standard deviation for the sampling distribution of the sample mean? b) What is the probability of finding a random slice of pizza with a mass of less than 67.2 grams? c) What is the probability of finding a 20 random slices of pizza with a mean mass of less than 67.2 grams? d) What sample mean (for a sample of size 20) would represent the bottom 15% (the 15th percentile)? grams
Mathematics
1 answer:
Alexxx [7]2 years ago
7 0

Answer:

<u>a. s.e. = 0.338</u>

<u>b. The  probability of finding a random slice of pizza with a mass of less than 67.2 grams is 0.5871 or 58.71%</u>

<u>c. The probability of finding a 20 random slices of pizza with a mean mass of less than 67.2 grams is 0.0694 or 6.94%</u>

d. <u>The sample mean of 62.75 would represent the 15th percentile</u>

Step-by-step explanation:

1. Let's review the information provided to us to answer the question properly:

μ of the mass of slices of pizza for a certain brand = 67.7 grams

σ of the mass of slices of pizza for a certain brand = 2.28 grams

2. For samples of size 20 pizza slices, what is the standard deviation for the sampling distribution of the sample mean?

Let's recall that the standard deviation of the sampling distribution of the mean is called the standard error of the mean and its formula is:

μσs.e.= √σ/n, where n is the sample size.

s.e. = √2.28/20

<u>s.e. = 0.338</u>

3. What is the probability of finding a random slice of pizza with a mass of less than 67.2 grams?

Let's find the z-score for X = 67.2, this way:

z-score = (X - μ)/σ

z-score = (67.2 - 67.7)/2.28

z-score = 0.5/2.28

z-score = 0.22 (rounding to the next hundredth)

Now, using the z-table, let's find p, the probability:

p (z = 0.22) = 0.5871

<u>The  probability of finding a random slice of pizza with a mass of less than 67.2 grams is 58.71%</u>

4.  What is the probability of finding a 20 random slices of pizza with a mean mass of less than 67.2 grams?

Let's use the central limit theorem to find the z-score, this way:

z-score = X - μ/s.e

z-score = 67.2 - 67.7/0.338

z-score = -0.5/0.338

z-score = - 1.48

Now, using the z-table, let's find p, the probability:

<u>p (z = -1.48) = 0.0694</u>

5. What sample mean (for a sample of size 20) would represent the bottom 15% (the 15th percentile)?

For p = 0.150, let's find the z-score:

z-score = - 2.17

z-score = X - μ/s.e

- 2.17 = (X - 67.7)/2.28

- 4.95 = X - 67.7

X = 67.7 - 4.95

X = 62.75 (rounding to the next hundredth)

<u>The sample mean of 62.75 would represent the 15th percentile</u>

You might be interested in
Alison wants to find the total cost of buying 4 adult admission tickets to an amusement park.identify the input and output
Keith_Richards [23]

If you are talking about a graph:

The input would be the number of adult tickets.

The output would be the amount of money.

If you talking about it normally:

The input would be the amount of money.

The output would be the number of adult tickets.

8 0
3 years ago
5,-15,35,55....<br> What is the common difference
harkovskaia [24]

Answer:

The common difference is -20

Step-by-step explanation:

Simply subtract 5 from -15

-15-5 = -20

3 0
2 years ago
Read 2 more answers
Find the equation of a line parallel to y - 5x = 10 that passes through the point (3, 10). (answer in slope-intercept form)
NeX [460]
So, a line parallel to <span>y - 5x = 10, will have the same slope as that equation, so what is that slope anyway?  let's solve for "y".

</span>\bf y-5x=10\implies y=5x+10\implies y=\stackrel{slope}{5}x\stackrel{y-intercept}{+10}
<span>
alrite, so the slope is 5 then, well, then the parallel line will have the same slope.

so, we're really looking for the equation of a line whose slope is 5 and runs through 3,10.


</span>\bf \begin{array}{lllll}&#10;&x_1&y_1\\&#10;%   (a,b)&#10;&({{ 3}}\quad ,&{{ 10}})&#10;\end{array}&#10;\\\\\\&#10;% slope  = m&#10;slope = {{ m}}= \cfrac{rise}{run} \implies 5&#10;\\\\\\&#10;% point-slope intercept&#10;\stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-10=5(x-3)&#10;\\\\\\&#10;y-10=5x-15\implies y=5x-5<span>
</span>
6 0
3 years ago
Read 2 more answers
Some drawbacks to renting can be: (Check all that apply) A. You build equity in a house B. Improvements made benefit the landlor
kkurt [141]

Answer:

A, B, C

Step-by-step explanation:

7 0
2 years ago
What property shows that 2/5 x 1 = 40/100
nekit [7.7K]
I believe the commutative property on multiplication

i hope this helped
5 0
3 years ago
Other questions:
  • Which number line represents all of the values of x for the equation x2 = 16? A number line is shown from negative 10 to 0 to po
    12·1 answer
  • Fanga ran 28 miles per in 4 hours She ran at a rate of how many miles per hour
    14·2 answers
  • A town has accumulated 2 inches of​ snow, and the snow depth is increasing by 6 inches every hour. A nearby town has accumulated
    9·1 answer
  • 2 (3u+7) = -4 (3-2u)
    6·1 answer
  • 344 thousands times 1/10
    8·1 answer
  • Factor this trinomial.<br> x2 + 2x-3
    7·1 answer
  • The model below is shaded to represent 7 3/10
    9·2 answers
  • Business owners use percents to calculate markup, discount, and sales tax. A shoe store owner buys a pair of shoes for $20. Ther
    12·1 answer
  • Bentley had $40 in birthday money in her piggy bank. She spent $10 on new flip-flops, then got $20 for her allowance and did not
    14·1 answer
  • Have to make the equation on the left look like the equation on the right. There are apparently only 2 steps but I can not figur
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!