Normal Distributions Finding Probabilities

According to the empirical rule, how much of the data falls within 3 standard deviations? 

• 25%

• 68%

• 95%

• 99.7%

The mean GPA of students in a course at UCDavis is 3.2 with a standard deviation of 0.3. What percent of students in the course have a GPA between  2.9 and 3.8? 

• 81.5%

• 47.5%

• 68%

• 95%

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 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?

• 68%

• 34%

• 16%

• 2.5%

What's the probability of 49 < x < 51 ?

(Mean = 50, Standard dev = 6.5)

• 0.1192

• 0.1251

• 0.1587

• 0.0875

The weight of infants at a daycare is normally distributed with a mean of 10 lbs and a standard deviation of 1.7 lbs. What is the probability a randomly selected baby weighs 8.1 lbs or less?

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.  What percent of households throw out fewer than 2 pounds of paper each week?

• 96.26%

• 48.13%

• 3.74%

• 1.87%

A continuous random variable is normally distributed with mean 145 and standard deviation is 5. Find P(136<X<140).

• 0.8054

• 0.8772

• 0.1228

• 0.1587

Suppose the heights of students in a high school are normally distributed with a mean of 65 inches and a standard deviation of 3 inches. What is the probability that a randomly selected student is taller than 70 inches?

• 0.0013

• 0.0228

• 0.0668

• 0.1587

A manufacturer contracts to supply ball bearings with diameters between 24.60mm and 25.4mm. Product analysis indicates that the ball bearings manufactured have diameters that are normally distributed with a mean of 25.10mm and a standard deviation of .20mm. What percentage of ball bearings fail to satisfy the contract specifications?

• 92.7%

• 7.3%

• 48.2%

• 33.2%