Question: At one university there were 807 faculty members and research specialists in the College of Liberal Arts and Science in 1993; the list of faculty and their reported publications for 1992-1993 were available on the computer system. For each faculty member, the number of refereed publications was recorded. This number is not directly available on the database, so the investigator is required to examine each record separately. A frequency table for number of refereed publications is given for an SRS of 50 faculty members.

Refereed publications      0       1       2       3        4        5       6       7       8        9        10

Faculty members           28      4       3       4        4        2       1       0       2        1         1

a Plot the data using a histogram. Describe the shape of the data.

b Estimate the mean number of publications per faculty member and give a standard error for your estimate.

c Do you think that y from part (b) will be approximately normally distributed? Why, or why not?

d Estimate the proportion of faculty members with no publications and give a 95% Cl for your estimate.