Distribution Problems

Find the area of the shaded region if the z-score is 1.25

• 0.1056

• 0.8944

• 0.8849

• 0.1151

Find the area of the shaded region if the z-score is 0.75

• 0.2266

• 0.7734

• 0.758

• 0.242

A z-score tells you...

• the standard deviation of a sampling distribution.

• the original raw score on which it is based.

• if the distribution it comes from is normal.

• how many standard deviations away from the mean a score lies.

The GPAs of students are normally distributed at UCDavis with a mean of 3.2 and a standard deviation of 0.3. What is the probability that a student selected at random has a GPA between 2.9 and 3.8?

• .8185

• .4772

• .1359

• .8216

Fernando is 60 inches tall. The average height for his age and gender is normally distributed with a mean of 68 with a standard deviation of 6 inches. If a man is selected at random, what is the probability that he is shorter than Fernando?

• .5918

• .9082

• .4082

• .0918

A variable is normally distributed with mean 145 and standard deviation is 5. Find P(136<X<140).

• 0.8054

• 0.8772

• 0.1228

• 0.1587

The shelf life of a particular dairy product is normally distributed with a mean of 12 days and a standard deviation of 3 days. If a dairy product is randomly selected, what is the probability that it will be "spoiled" in 8 days or less?

• .0918

• .4082

• .5918

• .9082

Weights of NFL players are normally distributed with a mean of 230lbs and a standard deviation of 30lbs. If a player is chosen at random, what is the most he could weigh to be in the bottom 5% of NFL player weights?

• Approx. 280 lbs

• Approx. 181 lbs

• Approx. 171 lbs

• Approx. 215 lbs

Given a mean of 75 and a standard deviation of 7, what percentage of scores are greater than 68?

• 34%

• 84%

• 95%

• 68%

The mean number of accidents a week at a company is 6.4 with a standard deviation of 1.5. What is the probability of 7 or more accidents this week? Assume a Normal distribution.

• 0.3446

• 0.2856

• 0.4

• 0.6554