Introduction to Normal Distributions Assignment and Quiz 80%

A newborn who weighs 2,500 g or less has a low birth weight. Use the information on the right to find the z-score of a 2,500 g baby.

-2

What is the mean of the normal distribution shown below? -1 0 1 2

0

Cynthia's z-score is

0.2

Use the information given in the table on the right to complete each of the following statements. Brenda is 50 inches tall. Her z-score is

0.5

What is the z-score of a newborn who weighs 4,000 g?

1

Approximately % of 7-year-old children are taller than 51 inches.

16

The amount of daily time that teenagers spend on a brand A cell phone is normally distributed with a given mean = 2.5 hr and standard deviation = 0.6 hr. What percentage of the teenagers spend more than 3.1 hr? 5% 10% 16% 32%

16%

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? 16 oz 18 oz 20 oz 22 oz

18 oz

99.7% of all newborn babies in the United States weigh between _____ and ___

2000 5000

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 standard deviation of 4°. How many years had temperatures within one standard deviation of the mean? 20 25 28 35

25

95% of all newborn babies in the United States weigh between 1000 g1500 g2000 g2500 g3000 g and 4000 g4500 g5000 g5500 g6000 g.

2500 4500

In the United States, birth weights of newborn babies are approximately normally distributed with a mean of μ = 3,500 g and a standard deviation of σ = 500 g. According to the empirical rule, 68% of all newborn babies in the United States weigh between 1000 g1500 g2000 g2500 g3000 g and 4000 g4500 g5000 g5500 g6000 g.

3000 4000

What weight would give a newborn a z-score of −0.75? ___ grams

3125

99.7% of 7-year-old children are between ____inches and _____ inches tall.

43 55

95% of 7-year-old children are between inches and inches tall.

45 53

Zach has a z-score of -1.5. His height is inches.

46

According to the empirical rule, 68% of 7-year-old children are between inches and inches tall.

47 51

The average miles per gallon of a particular automobile model are approximately normally distributed with a given mean = 43.8 miles per gallon and standard deviation = 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% 75% 95% 100%

68%

Use the information on the right to determine which students will have positive z-scores. Aaliyah, who completed the exam in 55 minutes Benjamin, who completed the exam in 86 minutes Cynthia, who completed the exam in 72 minutes

Benjamin, who completed the exam in 86 minutes Cynthia, who completed the exam in 72 minutes

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? 16° 18° 27° 29°

NOT: 18°

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? 18° 19° 22° 30°

NOT: 18°

In the United States, birth weights of newborn babies are approximately normally distributed with a mean of μ = 3,500 g and a standard deviation of σ = 500 g. What percent of babies born in the United States are classified as having a low birth weight (< 2,500 g)? Explain how you got your answer.

The z-score for 2,500 g is -2.According to the empirical rule, 95% of babies have a birth weight of between 2,500 g and 4,500 g.5% of babies have a birth weight of less than 2,500 g or greater than 4,500 g.Normal distributions are symmetric, so 2.5% of babies weigh less than 2,500g.

The class scores of a history test have a normal distribution with a mean = 79 and a standard deviation = 7. If Opal's test score was 72, which expression would she write to find the z-score of her test score?

a

The weights of 2-pound bags of Best Dog Food are approximately normally distributed with a given mean Mu and standard deviation Sigma. According to the Empirical Rule, what percentage of the bags will have weights within 3 standard deviations of the mean? 47.5% 68% 95% 99.7%

99.7%

The heights of a certain type of tree are approximately normally distributed with a mean height = 5 ft and a standard deviation = 0.4 ft. Which statement must be true? A tree with a height of 5.4 ft is 1 standard deviation below the mean. A tree with a height of 4.6 ft is 1 standard deviation above the mean. A tree with a height of 5.8 ft is 2.5 standard deviations above the mean. A tree with a height of 6.2 ft is 3 standard deviations above the mean.

A tree with a height of 6.2 ft is 3 standard deviations above the mean.