Statistics Normal Calculations

The weights of paper discarded each week by households are normally distributed with a mean of 9.43 pounds and a standard deviation of 4.17 pounds. The top 10% of households discard at least (a)   pounds of paper.

The lengths of human pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days. How long is a pregnancy if it is considered one of the top 20% in length?

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

What shape is a normal distribution curve?

What is the z-score for the mean?

If I have a positive z-score, I scored ABOVE or BELOW the mean?

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?

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 22%.

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?

A study of the amounts of time college freshmen study each week found that the times are normally distributed with a mean of 7.06 hours and a standard deviation of 2.32 hours. How many hours would the "fastest" 5% of students spend on homework?