Normal Distributions Area

If I tell you that you scored at the 55th percentile on your final exam, you would know:

• 55% of the class scored the same or worse than you did

• You earned a 55% on the exam

• You failed the exam

• 45% of the class scored worse than you did

In a survey of men in the United States (ages 20-29), the mean height was 69.6 inches with a standard deviation of 3.0 inches. Find the minimum height in the top 17.5%. (Hint, inverse normal uses the area to the left of the value)

• 69.98 in

• 71.18 in

• 72.40 in

• 73.01 in

Suppose the amount of soda in a can is normally distributed; the mean is 16 oz and you know that the 22nd percentile is 15.69 oz. What is the standard deviation? (hint: find the z score first)

• 0.4 oz

• -0.4 oz

• 40 oz

• 80 oz

The shelf life of a particular dairy product is normally distributed with a mean of 12 days and a standard deviation of 3 days.

About what percent of the products last between 12 and 15 days? (Hint: Don't use inverse normal)

• 68%

• 34%

• 16%

• 2.5%

In a Standard Distribution Curve, find the z-score for the lowest 7th percentile.

The scoring of modern IQ is such that Intelligence Quotients (IQs) have a normal distribution of μ= 100 and 𝞂 = 15.

Mensa International is a non-profit organization that accepts only people with IQ score within the top 2%. What level of IQ qualifies one to be a member of Mensa?

• 115

• 130.8

• 145.5

• 120

At Chili's, the average wait time to receive your meal is 22 minutes with a standard deviation of 9 minutes. What is the wait time for the top 12% ? Round to the nearest minute.

• 39 minutes

• 37 minutes

• 33 minutes

• 31 minutes

Suppose the amount of soda in a can is normally distributed; the mean is 16 oz and standard deviation is 0.4 oz. How much soda is in the heaviest 3% of cans?

If the value we are looking for is the same as the mean, the value of z is:

• Not enough information

• Positive

• Negative

• 0

Z-score of 2.5 on an IQ test is considered a genius (mean=100, SD=16). What score makes someone a genius? (Hint: SOLVE for X - use the formula)

• 89.2

• 130

• 99.38

• 140