honeycfa

Monthly sales of hot water heaters are approximately normally distributed with a mean of 21 and a standard deviation of 5. What is the probabilility of selling 12 hot water heaters or less next month?

A) 3.59%.

B) 1.80%.

C) 96.41%.

---

Z = (12 – 21) / 5 = -1.8

From the cumulative z-table, the probability of being more than 1.8 standard deviations below the mean, probability x < -1.8, is 3.59%.

honeycfa

The owner of a bowling alley determined that the average weight for a bowling ball is 12 pounds with a standard deviation of 1.5 pounds. A ball denoted “heavy” should be one of the top 2% based on weight. Assuming the weights of bowling balls are normally distributed, at what weight (in pounds) should the “heavy” designation be used?

A) 14.22 pounds.

B) 14.00 pounds.

C) 15.08 pounds.

---

The first step is to determine the z-score that corresponds to the top 2%. Since we are only concerned with the top 2%, we only consider the right hand of the normal distribution. Looking on the cumulative table for 0.9800 (or close to it) we find a z-score of 2.05. To answer the question, we need to use the normal distribution given: 98 percentile = sample mean + (z-score)(standard deviation) = 12 + 2.05(1.5) = 15.08.