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AP Statistics : AP Statistics

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4 Diagnostic Tests 140 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #2 : How To Find Standard Deviation Of A Random Variable

Consider the discrete random variable $\small X$ that takes the following values with the corresponding probabilities:

$\small X=1$ with $\small \small P(X=1)=\frac{1}{4}$
$\small X=2$ with $\small \small P(X=2)=\frac{1}{4}$
$\small X=3$ with $\small \small P(X=3)=\frac{1}{4}$
$\small X=4$ with $\small P(X=4)=\frac{1}{4}$

Compute the expected value of the distribution.

Possible Answers:

$\small 2$

$\small 3$

$\small 10$

$\small 2.5$

Correct answer:

$\small 2.5$

Explanation:

The expected value is computed as

$\small \mathbb{E}[X]=\small \sum_{x} xP(X=x)$

for any values of x that the random variable takes.

So we have

$\small \small \mathbb{E}[X]= \frac{1}{4}\cdot 1+\frac{1}{4}\cdot 2+\frac{1}{4}\cdot 3+\frac{1}{4}\cdot 4$

$\small =\frac{10}{4}=2.5$

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Example Question #4 : How To Find Standard Deviation Of A Random Variable

The average number of calories in a Lick Yo' Lips lollipop is 210 , with a standard deviation of . The calories per lollipop are normally distributed, so what percent of lollipops have more than 225 calories?

Possible Answers:

$6.68\%$

$47.9\%$

$3.56\%$

$4.57\%$

$45.7\%$

Correct answer:

$6.68\%$

Explanation:

The random variable X = number of calories per lollipop, so the answer is

$P(\mbox{Number of Calories} > 225)$ or

$P(X > 225) = P(Z > \frac{(225-210)}{10}) = P(Z > 1.5) = 1- 0.9332 = 0.0668.$

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Example Question #141 : Ap Statistics

Robert's work schedule for next week will be released today. Robert will work either 45, 40, 25, or 12 hours. The probabilities for each possibility are listed below:

45 hours: 0.3

40 hours: 0.2

25 hours: 0.4

12 hours: 0.1

What is the standard deviation of the possible outcomes?

Possible Answers:

13.5

11.07

32.7

122.61

35.8

Correct answer:

11.07

Explanation:

There are four steps to finding the standard deviation of random variables. First, calculate the mean of the random variables. Second, for each value in the group (45, 40, 25, and 12), subtract the mean from each and multiply the result by the probability of that outcome occurring. Third, add the four results together. Fourth, find the square root of the result.

$(45-32.7)^{2}(0.3)=45.38$

$(40-32.7)^{2}(0.2)=10.66$

$(25-32.7)^{2}(0.4)=23.72$

$(12-32.7)^{2}(0.1)=42.85$

45.38+10.66+23.72+42.85=122.61

$\sqrt{}122.61=11.07$

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Example Question #72 : Statistical Patterns And Random Phenomena

Possible Answers:

Correct answer:

Explanation:

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Example Question #81 : Statistical Patterns And Random Phenomena

Possible Answers:

Correct answer:

Explanation:

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Example Question #1 : How To Do The Linear Transformation Of A Random Variable

Variable has a Poisson distribution with a mean of . What is the variance of Variable ?

Possible Answers:

$\sigma^{2} = 105$

$\sigma^{2} = 130$

$\sigma^{2} = 400$

$\sigma^{2} = 25$

$\sigma^{2} = 20$

Correct answer:

$\sigma^{2} = 25$

Explanation:

Because has a Poisson distribution we know that:

$E(A)=\mu$ and

$V(A)=\sigma^2=\mu$ .

Therefore, since we are given the mean of 25, we can find its variance to also be 25.

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Example Question #1 : How To Use Tables Of Normal Distribution

Find the area under the standard normal curve between Z=1.5 and Z=2.4.

Possible Answers:

0.3220

0.0822

0.9000

0.0768

.0586

Correct answer:

.0586

Explanation:

$Z_{2.4}=.9918$

$Z_{1.5}=.9332$

.9918-.9332=.0586

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Example Question #1 : Normal Distribution

Alex took a test in physics and scored a 35. The class average was 27 and the standard deviation was 5.

Noah took a chemistry test and scored an 82. The class average was 70 and the standard deviation was 8.

Show that Alex had the better performance by calculating -

1) Alex's standard normal percentile and

2) Noah's standard normal percentile

Possible Answers:

Alex = .901

Noah = .926

Alex = .923

Noah = .911

Alex = .855

Noah = .844

Alex = .945

Noah = .933

Alex = .778

Noah = .723

Correct answer:

Alex = .945

Noah = .933

Explanation:

Alex -

$Z=\left ( 35-27\right )/5 = 1.6 = .945$ on the z-table

Noah -

$Z=\left ( 82-70\right )/8=1.5=.933$ on the z-table

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Example Question #2 : How To Use Tables Of Normal Distribution

When

$\mu=19$

and

$\sigma=6$

Find

$P\left ( 12< x< 25\right )$ .

Possible Answers:

.68

.76

.81

.61

.72

Correct answer:

.72

Explanation:

$Z_{12}=\left ( 12-19\right )\div6=-1.17$

$p_{-1.17}=.121$

$Z_{25}=\left ( 25-19\right )\div6=1$

$p_{1}=.8413$

$P\left ( 12< x< 25\right )=.8413 - .121 = .7203$

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Example Question #2 : Normal Distribution

Arrivals to a bed and breakfast follow a Poisson process. The expected number of arrivals each week is 4. What is the probability that there are exactly 3 arrivals over the course of one week?

Possible Answers:

$19.5\%$

$41\%$

$12.4\%$

$9.23\%$

$63.5\%$

Correct answer:

$19.5\%$

Explanation:

$P(X=3)=\frac{(\lambda t)^n}{n!}e^{-\lambda t}=\frac{(4\cdot 1)^3}{3!}e^{-4\cdot 1}=19.5\%$

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AP Statistics : AP Statistics

Study concepts, example questions & explanations for AP Statistics

All AP Statistics Resources

Example Questions

Example Question #2 : How To Find Standard Deviation Of A Random Variable

Example Question #4 : How To Find Standard Deviation Of A Random Variable

Example Question #141 : Ap Statistics

Example Question #72 : Statistical Patterns And Random Phenomena

Example Question #81 : Statistical Patterns And Random Phenomena

Example Question #1 : How To Do The Linear Transformation Of A Random Variable

Example Question #1 : How To Use Tables Of Normal Distribution

Example Question #1 : Normal Distribution

Example Question #2 : How To Use Tables Of Normal Distribution

Example Question #2 : Normal Distribution

All AP Statistics Resources

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