Normal Distributions

The distribution of household incomes in a small town is strongly skewed to the right. The mean income is $42,000 and the standard deviation is $24,000. The Ames family’s household income is $60,000. The z-score for the Ames family’s income is

• -0.75

• 0.3

• 0.75

• 0.86

• None of these, because z-score cannot be used unless the distribution is Normal

Jack and Jill are both enthusiastic players of a certain computer game. Over the past year, Jack’s mean score when playing the game is 12,400 with a standard deviation of 1500. During the same period, Jill’s mean score is 14,200, with a standard deviation of 2000. They devise a fair contest: each one will play the game once, and they will compare z-scores. Jack gets a score of 14,000, and Jill gets a score of 16,000. Who won the contest, and what were each of their z-scores?

• Jack’s z = 1.07; Jill’s z = 1.11; Jill wins the contest

• Jack’s z = 1.07; Jill’s z = 0.90; Jack wins the contest

• Jack’s z = 0.94; Jill’s z = 1.11; Jill wins the contest

• Jack’s z = 0.94; Jill’s z = 0.90; Jack wins the contest

• Jack’s z = 0.81; Jill’s z = 0.99; Jill wins the contest

If 30 is added to every number on a list, the only one of the following that is not changed is

• the mean.

• the mode.

• the 75th percentile.

• the median.

• the standard deviation.

Which of the following dot plots would best be approximated by a Normal distribution?

• A

• B

• C

• D

• E

Birthweights at a local hospital have a Normal distribution with a mean of 110 oz. and a standard deviation of 15 oz. The proportion of infants with birthweights between 125 oz. and 140 oz. is about

• 0.136

• 0.270

• 0.477

• 0.636

• 0.819

A company produces ceramic floor tiles that are supposed to have a surface area of 16.0 square inches. Due to variability in the manufacturing process, the actual surface area has a Normal distribution with a mean of 16.1 square inches and a standard deviation of 0.2 square inches. The proportion of tiles produced by the process with surface area less than 16.0 square inches is

• 0.1915

• 0.3085

• 0.3173

• 0.4115

• 0.6915

The scores on a university examination are Normally distributed with a mean of 62 and a standard deviation of 11. If the bottom 5% of students will fail the course, what is the lowest mark that a student can have and still be awarded a passing grade?

• 40

• 43

• 44

• 57

• 62

A company produces packets of soap powder labeled "Giant Size 32 Ounces." The actual weight of soap powder in a box has a Normal distribution with a mean of 33 oz. and a standard deviation of 0.8 oz. What proportion of packets are underweight (i.e., weigh less than 32 oz.)?

• 0.106

• 0.115

• 0.159

• 0.212

• 0.841

The time to complete a standardized exam is approximately Normal with a mean of 70 minutes and a standard deviation of 10 minutes. How much time should be given to complete the exam so that 80% of the students will complete the exam in the time given?

• 61.6 minutes

• 78.4 minutes

• 79.8 minutes

• 84 minutes

• 92.8 minutes

Entomologist Heinz Kaefer has a colony of bongo spiders in his lab. There are 1000 adult spiders in the colony, and their weights are Normally distributed with mean 11 grams and standard deviation 2 grams. About how many spiders are there in the colony which weigh more than 12 grams?

• 117

• 160

• 310

• 690

• 840