Question

A teacher gives the following assignment to 200 students: Check the local newspaper every morning for a week and count how many times the word “gun” is mentioned on the “local news” pages. At the end of the week, the students report their totals. The mean result is 85, with a standard deviation of 8. The distribution of scores is normal. a. How many students would be expected to count fewer than 70 cases? b. How many students would be expected to count between 80 and 90 cases? c. Karen is a notoriously lazy student. She reports a total of 110 cases at the end of the week. The professor tells her that he is convinced she has not done the assignment, but has simply made up the number. Are his suspicions justified?

Answer 1

(a)

The z-score for X = 70 is

The probability that student count fewer than 70 cases is

P(X < 70) = P(z < -1.875) = 0.0304

The number of students would be expected to count fewer than 70 cases is

200 * .0304 = 6.08

For finding probability excel function used "=NORMSDIST(-1.875)"

(b)

The z-score for X = 80 is

The z-score for X = 90 is

The probability that students count between 80 and 90 cases is

The number of  students would be expected to count between 80 and 90 cases is

200 * 0.468 = 93.6

For finding probability excel function used "=NORMSDIST(0.625)-NORMSDIST(-0.625)"

(c)

The z-score for X = 110 is

The probability of getting 110 or more cases is

Since this probability is less than 0.05 so his suspicions are justified.