Algebra 2 Probability, Normal Distribution and Z Score

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%

Assume that the salaries of elementary school teachers in the United States are normally distributed with a

mean of $32,000 and a standard deviation of $3000. If a teacher is selected at random, find the probability that

he or she makes more than $36,000.

• 0.9802

• 0.2113

• 0.0918

• 0.9827

The lengths of pregnancies of humans are normally distributed with a mean of 268 days and a standard

deviation of 15 days. Find the probability of a pregnancy lasting more than 300 days.

• 0.0166

• 0.9834

• 0.2375

• 0.3189

A data set has a mean of 290 and a standard deviation of 20. Calculate the z-score for 265.

• 298

• 296

• 220

• 380

The volumes of soda in quart soda bottles can be described by a Normal model with a mean of 32.3 oz and a standard deviation of 1.2 oz. What percentage of bottles can we expect to have a volume less than 32 oz?

• 0.4013

• 0.2403

• 0.5204

• 0.1407

A normal distribution has a mean of 290 and a standard deviation of 23. What data point is found at the 18th percentile?

• 269

• 254

• 244

• 261

In a normal distribution, what are the z scores for the middle 82% of data?

• -2.24

• +/- 1.75

• +/- 1.64

• +/- 1.34

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 is the z-score for 1200 pounds? What percentile is this?

• z=2.27, 99th percentile

• z-=2.27, 1st percentile

• z=-2.27, 1st percentile

• z=-2.27, 99th percentile

What is the area under the Normal curve that falls to the left of z = 1.23?