Statistics Quiz: Using Normal Distributions To Estimate Populations

Normal data have mean 500 and SD 100. What score is the 90th percentile?

A normal data set has mean 100 and SD 15. Estimate the percentage of values from 85 to 130.

Which clue most strongly suggests a normal model is inappropriate?

In a normal distribution, the area below z=1.28 is 0.90. What percentage is between z=-1.28 and z=1.28?

For normal data, mean 68 and SD 4. Estimate the percentile of 75.

A machine fills cereal boxes, and the fill weights are approximately normal. The mean fill weight is $\mu=500$ g with standard deviation $\sigma=10$ g. Approximately what percent of boxes have fill weights between 490 g and 510 g? (Use the empirical rule.)

Scores on a standardized exam are designed to be approximately normal. Suppose scores have mean $\mu=70$ and standard deviation $\sigma=10$. Approximately what percent of students score between 60 and 80? (Use the empirical rule.)

A factory produces metal rods whose lengths are roughly symmetric and bell-shaped, so a normal model is appropriate. Rod lengths have mean $\mu=50$ cm and standard deviation $\sigma=2$ cm. Approximately what percent of rods are longer than 54 cm? (Use the empirical rule approximation.)

A quality-control measurement is approximately normal. The measurement has mean $\mu=200$ units and standard deviation $\sigma=5$ units. Approximately what percent of measurements are below 190 units? (Use the empirical rule.)

The diameters of ball bearings from a well-controlled process are roughly symmetric and bell-shaped, so assume a normal model. Diameters have mean $\mu=10.0$ mm and standard deviation $\sigma=0.2$ mm. Approximately what percent of bearings have diameter greater than 10.4 mm? (Use the empirical rule.)

IQ scores are often modeled as approximately normal. Suppose IQ has mean $\mu=100$ and standard deviation $\sigma=15$. Approximately what percent of people have IQ between 85 and 115? (Use the empirical rule.)

Adult heights in a large population are roughly bell-shaped, so using a normal model is reasonable. Suppose heights have mean $\mu=170$ cm and standard deviation $\sigma=6$ cm. Approximately what percent of adults are shorter than 164 cm? (Use the empirical rule.)

Scores on a standardized math assessment are modeled well by a normal distribution (approximately symmetric and bell-shaped). The scores have mean $\mu = 70$ and standard deviation $\sigma = 10$. Approximately what percent of students score between 60 and 80? (Use the empirical rule.)

The time it takes a printer to complete a certain job is approximately normal (based on many runs, the distribution is roughly symmetric and bell-shaped). The times have mean $\mu = 30$ seconds and standard deviation $\sigma = 2$ seconds. Approximately what percent of jobs take between 28 and 32 seconds? (Use the empirical rule.)

A set of exam scores is modeled as approximately normal (roughly symmetric and bell-shaped) with mean $\mu = 500$ and standard deviation $\sigma = 100$. Approximately what percent of scores are below 700? (Use the empirical rule.)

A company reports that the diameters of its ball bearings are approximately normal (roughly symmetric and bell-shaped). The diameters have mean $\mu = 10.00$ mm and standard deviation $\sigma = 0.02$ mm. Approximately what percent of ball bearings have diameter above $10.02$ mm? (Use the empirical rule.)

A large set of reading assessment scores is approximately normal (bell-shaped). Scores have mean $\mu=500$ and standard deviation $\sigma=100$. Approximately what percent of students score between 300 and 700? (Use the empirical rule.)

The time (in minutes) it takes trained workers to complete a routine assembly task is roughly bell-shaped, so a normal model is reasonable. Completion times have mean $\mu=30$ and standard deviation $\sigma=4$. Approximately what percent of workers finish the task between 26 and 34 minutes? (Use the empirical rule.)

The diameters of ball bearings produced by a machine are approximately normally distributed. The diameters have mean $\mu=10.00$ mm and standard deviation $\sigma=0.05$ mm. Approximately what percent of ball bearings have diameter above 10.10 mm? (Use the empirical rule.)

The fill weights of a snack package are monitored and are known to be approximately normal (bell-shaped with no strong outliers). The weights have mean $\mu=50$ g and standard deviation $\sigma=2$ g. Approximately what percent of packages have a fill weight between 48 g and 52 g? (Use the empirical rule.)