Unit 4 test: Probability, Random Variables and Distributions

A computer simulated a random process 500 times. The event of interest happened in 43 of the trials. Estimate the probability of the event.

A player wins a game with probability $0.62$, independently each time she plays. Which assignment of random digits correctly simulates one game?

For events $A$ and $B$, $P(A) = 0.40$, $P(B) = 0.35$ and $P(A \text{ and } B) = 0.15$. Find $P(A \text{ or } B)$.

A survey of 150 students at a school recorded class and preferred pet.

One of these students is chosen at random. Given that the student prefers cats, what is the probability that the student is a senior?

Factory A makes $70\%$ of a company's phone chargers and factory B makes $30\%$. Of the chargers from A, $2\%$ are defective; of those from B, $5\%$ are defective. A randomly chosen charger is defective. What is the probability it came from factory B? Give an exact fraction or a decimal rounded to 3 places.

For events $A$ and $B$, $P(A) = 0.5$, $P(B) = 0.3$ and $P(A \mid B) = 0.5$. Which statement must be true?

A website's login server fails on any given day with probability $0.05$, independently from day to day. Find the probability that it fails on at least one of 6 days. Round to 4 decimal places.

The number of people $X$ in a randomly chosen car passing a checkpoint has the distribution below, with one probability missing.

Find $P(X \ge 3)$.

For the distribution in the previous problem, find the mean number of people per car.

For the same distribution, find the standard deviation of the number of people per car. Round to 2 decimal places.

The daily high temperature $C$ in a city in May has mean $20$ and standard deviation $5$ degrees Celsius. The Fahrenheit temperature is $F = 32 + 1.8C$. What are the mean and standard deviation of $F$?

$X$ and $Y$ are independent random variables with $\sigma_X = 5$ and $\sigma_Y = 12$. Find the standard deviation of $X - Y$.

A spinner lands on red with probability $0.25$. It is spun 12 times, independently. Find the probability that it lands on red exactly 4 times. Round to 4 decimal places.

In a large state, $35\%$ of registered voters support a proposed law. In a random sample of 400 registered voters, let $X$ = the number who support it. What are the mean and standard deviation of $X$?

About $10\%$ of the tickets in a scratch-off game are winners, independently. Let $X$ = the number of tickets you buy until you get your first winner. Find $P(X = 5)$. Round to 4 decimal places.