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.

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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

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%