Take this Exam: AP Statistics — probability and sampling distributions | Zestly

Question 1

In an invented test each question offers five options and a candidate guesses at random throughout. What is the probability that the first question she answers correctly is the third one?

Accepted Answer

$(0.8)^2 \cdot 0.2$

Answer

$(0.8)^3 \cdot 0.2$

Answer

$(0.2)^2 \cdot 0.8$

Answer

$(0.2)^3$

Question 2

In an invented pair of tests, scores on the first are roughly normal with a mean of 70 and a standard deviation of 10, and scores on the second are roughly normal with a mean of 80 and a standard deviation of 5. A candidate scores 85 on each. On which test is that the stronger performance, measured against the others who sat it?

Accepted Answer

On the first, where the score stands one and a half standard deviations above the mean rather than one

Answer

On the second, because 85 sits in a distribution whose centre is already higher

Answer

Neither, since the raw score is 85 in both cases and the two performances are therefore equal

Answer

It cannot be judged, because the two tests are measured on different scales

Question 3

In an invented survey, the number of books adults in a large city read last year is strongly right-skewed: most read a handful and a few read a great many. A researcher takes many random samples of forty adults and records the mean of each sample. What does the central limit theorem entitle her to say?

Accepted Answer

That the collection of sample means will itself be roughly normal in shape, despite the skew in the individual counts

Answer

That the distribution of book counts across the city will become roughly normal once enough samples have been taken

Answer

That any one sample of forty will have a roughly normal shape, because forty is a reasonably large sample

Answer

That nothing follows, because the theorem applies only when the population is itself normal

Question 4

In an invented study the standard deviation of the sample mean is 2 when the sample size is one hundred. What does it become if the sample size is raised to four hundred and the population is unchanged?

Answer

8

Answer

0.5

Answer

1

Answer

4

Question 5

In an invented school of four hundred pupils, half study a foreign language and a quarter play in the orchestra. Among the orchestra members, half study a foreign language. Are the two characteristics independent, and how can that be told?

Answer

They are dependent, because a pupil can belong to both groups and the two groups therefore overlap

Answer

They are independent, because the proportion studying a language is the same among orchestra members as it is in the school as a whole

Answer

They are dependent, because the orchestra is a quarter of the school while half of its members study a language, and those two fractions differ

Answer

They are independent, because playing in an orchestra and studying a language are separate activities chosen for separate reasons