Normal Distributions Answers

A set of data is normally distributed with a mean of 75 and a standard deviation of 3. What percent of the data is in the interval 72–78?

The heights of a certain group of adult males was found to be normally distributed. The mean height is 170 cm with a standard deviation of 6 cm. In a group of 1200 of these males, about how many would be more than 164 cm tall?

Daytime high temperatures in New York in February are normally distributed with an average of 30.2º and a standard deviation of 8.5º.Estimate the probability that the temperature on a given day in February is 22º or lower.

Daytime high temperatures in New York in February are normally distributed with an average of 30.2º and a standard deviation of 8.5º.Estimate the probability that the temperature on a given day in February is 39º or higher.

In a certain normal distribution of scores, the mean is 40 and the standard deviation is 3. Find the z-score corresponding to a score of 54.

A set of data is normally distributed with a mean of 455 and a standard deviation of 25. What percent of the data is in the interval 405–455?

Suppose that the heights of adult women are normally distributed with = 65 inches and = 2.5 inches. Find the probability that a randomly chosen woman is taller than 65 inches.

A set of data is normally distributed with a mean of 86 and a standard deviation of 1.5. What percent of the data is in the interval 86–87.5?

A sample of restaurants in a city showed that the average cost of a glass of iced tea is $1.25 with a standard deviation of 7¢. If a new restaurant charges a price for iced tea that has a z-value of -1.25, then what is the tea’s actual cost?

A normal distribution is bell-shaped and symmetric about its mean.