Question

Statistics for behavioral science (show work)

Criterion: Solve problems with information about normal distributions and probabilities.

Instructions: Read the following and answer the questions.

Judging the humorousness of “lawyer” jokes. Stillman, Baumeister, and DeWall (2007) conducted a study where participants listened to a variety of jokes. To determine how funny the jokes were, the researchers asked a group of 86 undergraduates to rate the jokes on a scale from 1 (very unfunny) to 21 (very funny). Participants rated a “lawyer joke” as one of the funniest jokes, with a rating of 14.48 ± 4.38 (M ± SD).

Assuming that these data are normally distributed,

the researchers asked a group of 86 undergraduates to rate the jokes on a scale from 1 (very unfunny) to 21 (very funny). Participants rated a “lawyer joke” as one of the funniest jokes, with a rating of 14.48 ± 4.38 (M ± SD).

Assuming that these data are normally distributed,

1. What was the rating that marks the cutoff for the top 10% of participant ratings for this joke?
2. How many of the 86 undergraduates gave the joke a rating of at least 10?

3. What was the rating that marks the cutoff for the top 10% of participant ratings for this joke?
4. How many of the 86 undergraduates gave the joke a rating of at least 10?

Answer 1

The cut off for the top 10% of participants rating for this joke will be the value corresponding to the 90th percentile.

Let X be the cut-off.

The z score for this cut off value will be

The z score corresponding to a p-value of 0.9 is 1.28

Putting the value of z, we have

Hence, the cutoff rating for the top 10% of the ratings = 20.086

The probability that the rating was at least 10 is given by

Hence, 85% of the participants gave the joke a rating of at least 10.

85 % of 86 = 73.10

Hence, 73 participants gave the joke a rating of at least 10.

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