AP Statistics: Normal Distribution Quiz

Questions and Answers

If the manager's belief is correct, which of the following intervals of weights will contain the largest proportion of the candies in the distribution of weights?

620 mg to 660 mg

660 mg to 700 mg

740 mg to 780 mg

700 mg to 740 mg (correct)

680 mg to 720 mg

What is the probability that at least 8 of the 9 participants will correctly identify the tap water?

0.9805

0.0020

0.0195 (correct)

0.8889

0.9980

What is the expected value of the sum of the numbers on the two selected tags from the boxes?

13.5

14.5

29.0 (correct)

15.0

27.0

How many dice should the player choose to roll to maximize the chance of winning?

Two Signup and view all the answers

Based on the results, what is the best conclusion about the CD cover designs?

It is reasonable to conclude that the difference in sales was caused by the different cover designs because the cover designs were randomly assigned to stores. Signup and view all the answers

What is the standard deviation of the profit Y, given by the equation Y = 75X - 100?

$432 Signup and view all the answers

What is the standard deviation, in pounds, of the total weight W from two farms' fleece production?

sqrt(1.3^2 + 0.5^2) Signup and view all the answers

Study Notes

Quality Control in Candy Production

Weight of candies believed to be normally distributed with a mean of 720 mg.
The interval containing the largest proportion of candies is from 700 mg to 740 mg.

Blind Taste Test Probability

Conducted with 9 volunteers to distinguish between bottled and tap water.
Probability that at least 8 participants correctly identify tap water is 0.0195.

Expected Value of Random Draws

Two boxes with different tag numbers: 10 tags (1-10) and 8 tags (20-27).
Expected value of the sum of randomly drawn tags from both boxes is 29.0.

Carnival Game Strategy

Player must choose the number of dice (2, 4, 6, 8, or 10) to maximize chances of winning.
Best choice is to roll two dice to maximize the probability of getting a 1 or 2.

CD Cover Design Experiment

Comparison of two CD cover designs across 70 stores.
Conclusion: It is reasonable to attribute sales difference to the cover designs due to random assignment of designs to stores.

Profit Calculation in Concrete Sales

Probability distribution for cubic yards of concrete sold: X values of 10, 15, 20, 25, and 30 with corresponding probabilities.
Expected value of X is 19.25; standard deviation is 5.76.
Profit formula is Y = 75X - 100; the standard deviation of profit (Y) is $432.

Fleece Weight Analysis

Two farms producing fleece: Northern (mean 14.1 lbs, SD 1.3 lbs) and Western (mean 6.7 lbs, SD 0.5 lbs).
Total weight W from 10 Northern sheep and 15 Western sheep requires calculating standard deviation.
Standard deviation of W is determined by √(10(1.3)² + 15(0.5)²).

Description

Test your understanding of normal distribution with this AP Statistics quiz. Assess your skills in determining intervals that capture the largest proportion of a normally distributed dataset. Perfect for AP Stats preparation!