Normal Probability

The lengths of a machined component may be modelled by a Normal distribution with mean 12.7 cm and standard deviation 0.75 cm. Find the proportion between 12.5 cm and 13.5 cm.

The volumes of soda in quart soda bottles can be described by a Normal model with a mean of 32.3 oz and a standard deviation of 1.2 oz. What percentage of bottles can we expect to have a volume less than 32 oz?

• 0.4013

• 0.2403

• 0.5204

• 0.1407

A bank's loan officer rates applicants for credit. The ratings can be described by a Normal model with a mean of 200 and a standard deviation of 50. What percentage of ratings can be expected to be between 200 and 275?

• 0.4331

• 0.5671

• 0.3861

• 0.2987

A town's average snowfall is 48 inches per year with a standard deviation of 6 inches. Using a Normal model, what values should border the middle 50% snowfalls?

• 44 and 52 inches

• 42 and 54 inches

• 40 and 50 inches

• 40 and 60 inches

A town has a speed limit of 45 mph. If the speeds of cars traveling in the town can be described by a Normal model with a mean of 48 mph and a standard deviation of 3.5 mph, what percent of cars are exceeding the speed limit?

• 80.43%

• 19.56%

• 23.86%

• 75%

A town's average snowfall is 48 inches per year with a standard deviation of 6 inches. Using a Normal model, what percent of snowfall amounts will be between 40 and 50?

• 0.5393

• 0.4607

• 0.3719

• 0.7234

A standardized test has scores that can be described by a Normal model with a mean score was 100 points and a standard deviation of 10 points. What score is at the 25th percentile?

• 93.26

• 106.74

• 90.32

• 80

Tags

CCSS.HSF-LE.A.1B

A bank's loan officer rates applicants for credit. The ratings can be described by a Normal model with a mean of 200 and a standard deviation of 50. What is the rating which cuts off the bottom 20%?

• 157.92

• 242.08

• 189.34

• 190.60

What's the probability x < 13?

(Mean = 10, Variance = 4)

• 77.34%

• 22.66%

• 27.34%

• 06.68%

What's the probability x > 17?

(Mean = 15, Standard dev = 3)

• 74.86%

• 75.14%

• 25.14%

• 25.46%