Binomial and Normal Distributions: AP Statistics Math Test – PDF Download

AP Statistics Binomial Normal Test: questions 1–5

Question 1: Binomial setting (2 points)

Aisha surveys \(25\) students chosen at random from a school of \(2{,}400\) students. In the school, \(30\%\) of students walk to school. Let \(X\) be the number of surveyed students who walk. Explain why \(X\) is a binomial random variable and identify its parameters. (2 points)

Question 2: Binomial probabilities (3 points)

A carnival game is won with probability \(0.4\) on each independent play. Let \(X\) be the number of wins in \(10\) plays. Find:

1. \(P(X=4)\) (1 point)
2. \(P(X\le 2)\) (1 point)
3. \(P(X\ge 3)\) (1 point)

Question 3: Mean and spread (2 points)

About \(20\%\) of emails to a company are spam, independently. Let \(X\) be the number of spam emails among \(300\) received.

1. Find the mean and standard deviation of \(X\). (1 point)
2. Find the interval within \(2\) standard deviations of the mean and interpret it. (1 point)

Question 4: Reading a binomial graph (2 points)

The graph shows the distribution of the number \(X\) of correct answers on a \(5\)-question quiz, where each answer is correct with probability \(0.6\), independently.

1. What is the most likely value of \(X\), and what is its probability? (1 point)
2. Find \(P(X\ge 4)\). (1 point)

Question 5: Normal probabilities (3 points)

The net weight of a bag of trail mix is approximately normal with mean \(12.0\) ounces and standard deviation \(0.3\) ounce.

1. Find the proportion of bags that weigh less than \(11.5\) ounces. (1 point)
2. Find the proportion that weigh between \(11.8\) and \(12.4\) ounces. (2 points)

AP Statistics Binomial Normal Test: questions 6–8

Question 6: Percentile cutoff (2 points)

Reaction times of drivers are approximately normal with mean \(250\) milliseconds and standard deviation \(40\) milliseconds. A researcher wants a cutoff so that only the slowest \(5\%\) of drivers are above it. Find the cutoff. (2 points)

Question 7: Comparing z-scores (2 points)

On the reading test, Noah scored \(68\) (class mean \(60\), standard deviation \(5\)). On the science test, Noah scored \(590\) (class mean \(520\), standard deviation \(50\)). On which test did Noah do better relative to his classmates? Justify. (2 points)

Question 8: Normal approximation (4 points)

A coffee shop finds that \(35\%\) of customers order through its app, independently. On a day with \(180\) customers, let \(X\) be the number who order through the app. The graph shows the distribution of \(X\) with a normal curve.

1. Verify that a normal approximation is appropriate. (1 point)
2. Find the mean and standard deviation of \(X\). (1 point)
3. Use the normal model to approximate \(P(X\ge 72)\). (1 point)
4. Is it unusual for \(72\) or more customers to use the app? Explain. (1 point)

How to use this ap statistics binomial normal test

Take this ap statistics binomial normal test without notes, then grade it with the test answer key out of 20 points.

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