Suppose a market research firm is hired to have test audiences rate the scariness of horror films, on a scale from 0 to 100. Suppose that the mean scariness rating for all films is77and the standard deviation is4.

Suppose that the distribution of scariness ratings is known to be approximately normal in shape and a new film got a rating of82.

What is the standard score for the film?

Approximately, what is the film's estimated percentile rank?

Estimate the minimum rating a film would need to be in the top 3%

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Suppose eight test viewers are asked about the new film. On a scale from 0 to 25, these are the results:

TABLE 1

X f

6 4

12 2

21 2

What is the mean of variable X?

What is the median of variable X?

What is the 70^thpercentile?

If a person scored a 12 on X, what is their deviation from the mean?

If you picked one score at random from the scores described in TABLE 1, and used that one score to estimate the mean of all scores, how far off would you typically be?

What is the sum of squares of variable X?

What is the variance of variable X?

What is the shape of the distribution in TABLE 1?

If a person scored a 12, what is their estimated percentile rank?

What is the highest a person can score on X and still be in the bottom 17%?

What is the lowest a person can score on X and still be in the top 23%?

Suppose that six people rated a film, and these scores resulted:

5, 4, 93, 7, 35, 78

What is the median?

What is the percentile rank when X=5?

What is the 67^thpercentile?

What is the 89^thpercentile of the standard normal distribution?