﻿ Statistics

## MAT 120 Sample Statistics Test

1. [40 pts.] In a year-long study of rainfall, the number of days during which measurable amounts of precipitation fell was recorded for a random sample of 30 cities. The results are given here:

122, 87, 79, 108, 112, 85, 65, 78, 75, 92, 112, 82, 89, 81, 85, 113, 91, 102, 126, 109, 103, 85, 95, 103, 102, 81, 88, 109, 105, 84

Using an Excel spreadsheet perform the following activities.

a. (15 pts.) Find the mean, the standard deviation, and the five-number summary. Display all of these values to one decimal place.

b. (15 pts.) Create a grouped frequency distribution using midpoint values that are multiples of ten.

c. (10 pts.) Insert a chart illustrating the frequency distribution for this data.

2. [40 pts.] An experiment consisted of rolling a pair of tetrahedral (4-sided) dice 32 times and recording the sum of the dots (the dot sum) each time. Here are the results:

6, 4, 6, 6, 6, 4, 6, 6, 8, 4, 6, 2, 8, 6, 5, 7, 5, 5, 7, 4, 4, 7, 5, 8, 4, 5, 7, 2, 6, 2, 7, 6

Using an Excel spreadsheet perform the following activities.

a. (15 pts.) Find the mean, the standard deviation, and the five-number summary. Display all of these values to one decimal place.

b. (15 pts.) Create an ungrouped frequency distribution.

c. (10 pts.) Insert a chart illustrating the frequency distribution for this data.

3. [10 pts.] Among a population of field mice, the weights of pups at the time of weaning are normally distributed with an average mass of 11 grams with a standard deviation of 1.2 grams. A single pup is selected at random. Use the left-tail probability table to find the following probabilities:

a. (3 pts.) The probability that the pup has a mass less than or equal to 10 grams.

b. (3 pts.) The probability that the pup has a mass greater than or equal to 9.5 grams.

c. (4 pts.) The probability that the pup has a mass between 11.25 and 12.75 grams.

4. [10 pts] In a particular academic competition, each team is composed of 4 students. To be ranked as an advanced team, the team must have an average IQ of at least 120. To be ranked as an elite team, the team must have an average IQ of at least 140. Three students (with IQs of 110, 130, and 150 respectively) are looking for a fourth team member to complete their team.

a. (5 pts.) What is the minimum IQ needed if the team is to be ranked as an advanced team?

b. (5 pts.) What is the minimum IQ needed if the team is to be ranked as an elite team?