Normal Distributions Application

Find the area of the shaded region.

• 16%

• 84%

• 68%

• 34%

This data is normally distributed.  What percent of the data is in the shaded region?

• 68%

• 32%

• 95%

• 50%

A normal distribution has a mean of 61 and a standard deviation of 15. What is the median?

Mathematical Equivalence

ON

Between what two standard deviations of a normal distribution contain 68% of the data?

• one below and one above

• two below and two above

• two below and zero

• zero and two above

The average waist size for teenage males is 29 inches with a standard deviation of 1.4 inch. 
If waist sizes are normally distributed, estimate the proportion of teenagers who will have waist sizes greater than 31 inches?

• 92.4%

• 10.5%

• 16%

• 7.6%

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

• 130.75

• 145

• 120

What is the the total area under the standard normal distribution curve?

• 100

• 25

• .5

• 1

μ = 70 , σ = 8 , X = 50 . Find z score

• 2.5

• -2.5

• 5.2

• -5.2

The z-score represents.....

• the amount of standard deviations a data value is above or below the mean.

• the percentile the data value is above or below the mean.

• the amount of standard deviations a data value is above or below the median.

• the percent the data value is above or below the mean.

The distances male long jumpers for State College jump are approximately normal with a mean of 263 inches and a standard deviation of 14 inches.  
Suppose a male long jumper's jump ranked in the 75th percentile.  How long was his jump?

• 0.67 inch

• 263 inches

• 272.44 inches

• 277.25 inches