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AP Statistics with 6 Practice Tests

Martin Sternstein

Chapter 5

Sampling Distributions - all with Video Answers

Educators

Section 20

Quiz 20

01:39

Problem 1

Which of the following is a true statement?
(A) The area under a normal curve is always equal to $1, n o$ matter what the mean and standard deviation are.
(B) All bell-shaped curves are normal distributions for some choice of $\mu$ and $\sigma$.
(C) The smaller the standard deviation of a normal curve, the lower and more spread out the graph.
(D) Depending upon the value of the standard deviation, normal curves with different means may be centered around the same number.
(E) Depending upon the value of the standard deviation, the mean and median of a particular normal distribution may be different.

Jerrah Biggerstaff
Jerrah Biggerstaff
Numerade Educator
01:33

Problem 2

Populations $\mathrm{P}_{1}$ and $\mathrm{P}_{2}$ are normally distributed and have identical means. However, the standard deviation of $\mathrm{P}_{1}$ is
twice the standard deviation of $\mathrm{P}_{2}$. What can be said about
the percentage of observations falling within two standard deviations of the mean for each population?
(A) The percentage for $\mathrm{P}_{1}$ is twice the percentage for $\mathrm{P}_{2}$.
(B) The percentage for $\mathrm{P}_{1}$ is greater than but not twice as great as the percentage for $\mathrm{P}_{2}$.
(C) The percentage for $\mathrm{P}_{2}$ is twice the percentage for $\mathrm{P}_{1}$.
(D) The percentage for $\mathrm{P}_{2}$ is greater than but not twice as great as the percentage for $\mathrm{P}_{1}$.
(E) The percentages are identical.

Jerrah Biggerstaff
Jerrah Biggerstaff
Numerade Educator
01:35

Problem 3

Assume the given distributions are approximately normal.
A trucking firm determines that its fleet of trucks averages a
mean of 12.4 miles per gallon with a standard deviation of 1.2 miles per gallon on cross-country hauls. What is the probability that one of the trucks averages fewer than 10 miles per gallon?
(A) $P(z<-2.4)$
(B) $P(z<-2)$
(C) $P(z<10)$
(D) $P\left(z<\frac{10}{1.2}\right)$
(E) $P\left(z<\frac{12.4}{1.2}\right)$

Jerrah Biggerstaff
Jerrah Biggerstaff
Numerade Educator
01:19

Problem 4

Assume the given distributions are approximately normal.
An electronic product takes an average of 3.4 hours to move through an assembly line. If the standard deviation is 0.5 hours, what is the probability that an item will take between
3 and 4 hours to move through the assembly line?
(A) $P(3<z<4)$
(B) $P\left(\frac{3}{0.5}<z<\frac{4}{0.5}\right)$
(C) $P(3-3.4<z<4-3.4)$
(D) $P((3-3.4)(0.5)<z<(4-3.4)(0.5))$
(E) $P\left(\frac{3-3.4}{0.5}<z<\frac{4-3.4}{0.5}\right)$

Jerrah Biggerstaff
Jerrah Biggerstaff
Numerade Educator
01:19

Problem 5

Assume the given distributions are approximately normal.
An electronic product takes an average of 3.4 hours to move through an assembly line. If the standard deviation is 0.5 hours, what is the probability that an item will take between 3 and 4 hours to move through the assembly line?
(A) $P(3<z<4)$
(B) $P\left(\frac{3}{0.5}<z<\frac{4}{0.5}\right)$
(C) $P(3-3.4<z<4-3.4)$
(D) $P((3-3.4)(0.5)<z<(4-3.4)(0.5))$
(E) $P\left(\frac{3-3.4}{0.5}<z<\frac{4-3.4}{0.5}\right)$

Jerrah Biggerstaff
Jerrah Biggerstaff
Numerade Educator
01:46

Problem 6

Assume the given distributions are approximately normal.
One company produces movie trailers whose mean length is 150 seconds with a standard deviation of 40 seconds, while a second company produces movie trailers whose mean length is 120 seconds with a standard deviation of 30 seconds. What is the probability that the combined length of two randomly selected trailers, one produced by each company, will be less than three minutes?
(A) 0.000
(B) $P\left(z<\frac{180-270}{50}\right)$
(C) $P\left(z<\frac{180-270}{50}\right)$
(D) $P\left(z<\frac{180-270}{\sqrt{40+30}}\right)$
(E) $P\left(z<\frac{180-270}{\sqrt{\frac{1}{10}+\frac{1}{30}}}\right)$

Jerrah Biggerstaff
Jerrah Biggerstaff
Numerade Educator
01:35

Problem 7

Assume the given distributions are approximately normal.
Cucumbers grown on a certain farm have weights with a standard deviation of 2 ounces. What is the mean weight if $85 \%$ of the cucumbers weigh less than 16 ounces?
(A) $16-0.518$
(B) $16-0.85(2)$
(C) $16-1.036(2)$
(D) $16+0.85(2)$
(E) $16+1.036(2)$

Jerrah Biggerstaff
Jerrah Biggerstaff
Numerade Educator