introduction to normal distributions
The lengths of a lawn mower part are approximately normally distributed with a given mean mc021-1.jpg = 4 in. and standard deviation mc021-2.jpg = 0.2 in. What percentage of the parts will have lengths between 3.8 in. and 4.2 in.?
68%
The amount of daily time that teenagers spend on a brand A cell phone is normally distributed with a given mean u= 2.5 hr and standard deviation o = 0.6 hr. What percentage of the teenagers spend more than 3.1 hr?
16%
The weights of 2-pound bags of Best Dog Food are approximately normally distributed with a given mean mc020-1.jpg and standard deviation mc020-2.jpg. According to the Empirical Rule, what percentage of the bags will have lengths within 3 standard deviations of the mean?
99.7%
The heights of a certain type of tree are approximately normally distributed with a mean height mc018-1.jpg = 5 ft and a standard deviation mc018-2.jpg = 0.4 ft. Which statement must be true?
A tree with a height of 6.2 ft is 3 standard deviations above the mean.
The graph below shows two normal distributions. difference in means
15
What is the mean of the normal distribution shown below? blue peak 4
4
What is the mean of the normal distribution shown below? blue peak 0
0
The weights of boxes of candies produced in a factory are normally distributed with a mean weight of 16 oz and a standard deviation of 1 oz. What is the weight of a box of candies with a z-score of 2?
18 oz
The set of life spans of an appliance is normally distributed with a mean mc012-1.jpg = 48 months and a standard deviation mc012-2.jpg = 8 months. What is the z-score of an appliance that stopped working at 64 months?
2
The graph below shows the average daily temperatures on January 1 from 1900 to 1934 for city A. The mean of the temperatures in the chart is 24° with a standard deviation of 4°. Which temperature is within one standard deviation of the mean?
22, 25, 27 degrees
The annual salaries of all employees at a financial company are normally distributed with a mean of $34,000 and a standard deviation of $4,000. What is the z-score of a company employee who makes an annual salary of $54,000?
5
The average miles per gallon of a particular automobile model are approximately normally distributed with a given mean mc024-1.jpg = 43.8 miles per gallon and standard deviation mc024-2.jpg = 5.1 miles per gallon. What percentage of the automobiles have an average miles per gallon between 38.7 miles per gallon and 48.9 miles per gallon?
68%
The lengths of a certain species of fish are approximately normally distributed with a given mean mc019-1.jpg and standard deviation mc019-2.jpg. According to the Empirical Rule, what percentage of the fish will have lengths within 1 standard deviation of the mean?
68%
three different normal distributions
each distribution has the same mean and a different standard deviation
