Unit 9 test: Statistics and Probability

The weights of newborn babies at a hospital are approximately normal with mean $7.5$ pounds and standard deviation $1.1$ pounds. Use the 68–95–99.7 rule to estimate the percent of newborns who weigh between $6.4$ and $9.7$ pounds.

A population has mean $120$ and standard deviation $12$. What is the z-score of the value $102$?

The length of a phone call to a help desk is normally distributed with mean $8$ minutes and standard deviation $2$ minutes. Use the table to find the probability that a call lasts longer than $10.5$ minutes. Give a decimal to four places.

Test scores are normal with mean $75$ and standard deviation $10$. Use the table to find the probability that a randomly chosen score is between $70$ and $90$. Give a decimal to four places.

A town council randomly selects $5$ streets and surveys every household on those streets. What type of sample is this?

A college has $3{,}000$ students: $1{,}800$ undergraduates and $1{,}200$ graduate students. A stratified sample of $30$ students is chosen using proportional allocation. How many undergraduates are in the sample?

A radio host asks listeners to call in and say whether they support a new curfew law. Which kind of bias is most likely?

A researcher wants to know whether a new study app raises test scores. Which plan allows a cause-and-effect conclusion?

In an experiment, the treatment group's times were $22, 25, 19, 24, 20$ seconds and the control group's times were $26, 28, 24, 25, 27$ seconds. Find the difference in means (control minus treatment), in seconds.

In a randomization test with $1{,}000$ re-randomizations, $240$ produced a difference in means at least as large as the one observed. What should you conclude?

A random sample of $1{,}600$ voters is surveyed. Use $\text{ME} \approx \dfrac{1}{\sqrt{n}}$ to find the margin of error, as a percent.

In a random sample of $600$ adults, $60\%$ say they read the news daily. Use $\text{ME} \approx 2\sqrt{\dfrac{\hat{p}(1 - \hat{p})}{n}}$ to find the margin of error, as a percent rounded to the nearest tenth.

$P(A) = 0.3$, $P(B) = 0.25$ and $P(A \text{ and } B) = 0.1$. Find $P(A \text{ or } B)$.

A survey of $160$ people recorded whether they own a pet and whether they live in an apartment.

Find $P(\text{pet} \mid \text{apartment})$.

A box holds $7$ good batteries and $3$ dead ones. Two are chosen at random without replacement. What is the probability that both are good? Give a fraction.