Normal Distribution and Percentiles

In a factory, the weight of the concrete poured into a mold by a machine follows a normal distribution with a mean of 1150 pounds and a standard deviation of 22 pounds. What weight falls at the 50th percentile?

• 1106 pounds

• 1128 pounds

• 1150 pounds

• 1172 pounds

What is the area under the curve to the left of z = 0.55 ?

• .2912

• .5500

• .9394

• .7088

What is the area under the curve between z = 0 and z = 1.45?

• .9265

• .4265

• .4500

• .5000

Scores on a certain standardized test have a mean of 500, and a standard deviation of 100. What score would you need to fall at the 84th percentile?

• 84

• 400

• 500

• 600

SAT scores in New York are approximately Normally distributed with a mean of 1050 and a standard deviation of 55. About 2.5% of all test scores are less than what score?

• 940

• 1050

• 885

• 995

SAT scores in New York are approximately Normally distributed with a mean of 1050 and a standard deviation of 55. About 2.5% of all test scores are less than what score?

• 940

• 1050

• 885

• 995

At a high school, GPAs are normally distributed with a mean of 2.9 and standard deviation of 0.6. What GPA do you need to fall in the top 20%? The top 10%?

• 3.40 and 3.67

• 3.67 and 3.40

• 3.80 and 3.90

• 3.20 and 3.10

At a local high school, GPAs are normally distributed with a mean of 2.9 and standard deviation of 0.6. What is the z-score for the 80th percentile? What GPA falls at the 80th percentile?

• z= -0.84, A GPA of 3.40

• z= -0,84, A GPA of 0.8

• z= 0.84, A GPA of 3.80

• z= 0.84, A GPA of 3.40

What percent of the data is between 80 and 92 on the normal curve?

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