STAT 101: Chapter 5 HW

Assume the distribution of IQ scores for adults can be modeled with a normal distribution with a mean score of 100 points and a standard deviation of 10 points. What percentage of adults have an IQ score between 92 and 112 points?

67.30%

Assume the length of female humpback whales can be modeled with a normal distribution with a mean of 13.7 meters and a standard deviation of 0.5 meters. What percentage of female humpback whales will be shorter than 14 meters in length?

72.57%

Fill in the blank with the correct number: Assume the length of female humpback whales can be modeled with a normal distribution with a mean of 13.7 meters and a standard deviation of 0.5 meters. According to the Empirical Rule or 68-95-99.7 Rule, _______ percent of female humpback whales will have a length between 12.7 meters and 14.7 meters.

95

Fill in the blank with the correct number: Assume the lifespan of light bulbs manufactured by Bright Inc. can be modeled with a normal distribution with a mean of 300 days and a standard deviation of 40 days. According to the Empirical Rule or 68-95-99.7 Rule, __________ percent of light bulbs made by Bright Inc. will last between 220 and 380 days.

95

Fill in the blank with the correct number: Assume the weight of a certain breed of cow can be modeled with a normal distribution with a mean of 750 kg and a standard deviation of 30 kg. According to the Empirical Rule or 68-95-99.7 Rule, _________ percent of cows from this breed will weigh between 690 kg and 810 kg.

95

In a sample of 25 male newborns, the mean birth weight was 3.4 kg and the standard deviation was 0.35 kg. The z-score for a birth weight of 2.5 kg is __________. Round your answer to 2 decimal places.

-2.57

Assume the distribution of IQ scores for adults can be modeled with a normal distribution with a mean score of 100 points and a standard deviation of 10 points. What percentage of adults have an IQ score higher than 128 points?

0.26%

Assume the lifespan of light bulbs manufactured by Bright Inc. can be modeled with a normal distribution with a mean of 300 days and a standard deviation of 40 days. 20% of light bulbs produced by Bright Inc. survive less than how many days?

266.4 days

Assume the weight of bags of M&Ms can be modeled with the normal distribution with mean 50 grams and standard deviation 1 gram. According to the Empirical Rule or 68-95-99.7 rule, 68% of all M&M bags will have weights between _______ and 51 grams.

49

Assume the distribution of the height of adult females can be modeled with a normal distribution with mean 66 inches and standard deviation 3 inches. According to the Empirical Rule or 68-95-99.7 Rule, the center 95% of all women will have heights between _______ and 72 inches.

60

Assume the length of female humpback whales can be modeled with a normal distribution with a mean of 13.7 meters and a standard deviation of 0.5 meters. What percentage of female humpback whales are longer than 12.1 meters?

99.93%

Which part of the distribution is NOT affected by standardizing?

shape

The z-score for a particular observation is z = 0.4. This means the observation is

0.4 standard deviations above the mean.

For the remaining questions, use either a z-table or an applet or both to do the calculations. Depending on the method used, the final answer could be subject to a small amount of rounding error. Assume the lifespan of light bulbs manufactured by Bright Inc. can be modeled with a normal distribution with a mean of 300 days and a standard deviation of 40 days. What percentage of light bulbs produced by Bright Inc. will survive less than 200 days?

0.62%

The z-score for a particular observation is z = -1.2. This means the observation is

1.2 standard deviations below the mean.

In a sample of 25 male newborns, the mean birth weight was 3.4 kg and the standard deviation was 0.35 kg. The z-score for a birth weight of 4.0 kg is __________. Round your answer to 2 decimal places.

1.71

Assume the distribution of IQ scores for adults can be modeled with a normal distribution with a mean score of 100 points and a standard deviation of 10 points. 30% of adults will have an IQ score higher than what value?

105.2 points

Assume the distribution of IQ scores for adults can be modeled with a normal distribution with a mean score of 100 points and a standard deviation of 10 points. According to the Empirical Rule or 68-95-99.7 Rule, the middle 68% of all adults will have an IQ score between 90 and _______ points.

110

Assume the distribution of IQ scores for adults can be modeled with a normal distribution with a mean score of 100 points and a standard deviation of 10 points. 90% of adults will have an IQ score higher than what value?

112.8 points

Assume the length of female humpback whales can be modeled with a normal distribution with a mean of 13.7 meters and a standard deviation of 0.5 meters. 65% of female humpback whales are shorter than what length?

13.90 meters

A blowhole is a hole in a cliff that produces eruptions of water when the ocean swell hits the cliff. Below are 40 times (in seconds) between eruptions for the Kiama blowhole in Australia. blowhole.jpg Based on the output, it is reasonable to model the distribution of times between eruptions with a normal distribution.

False

Standardizing makes the following change(s) to a distribution: I. Shifts the distribution by subtracting the mean. II. Rescales the distribution by dividing by the standard deviation. III. Changes the skewness or symmetry of the distribution. IV. Creates outliers.

I and II

The height of adult women is thought to have a mean of 65 inches and a standard deviation of 2.5 inches. The height of adult men is thought to have a mean of 71 inches and a standard deviation of 3 inches. In the same family, the son is 73 inches tall and the daughter is 67 inches tall. Who is taller among their gender, the son or daughter?

The daughter

The height of adult women is thought to have a mean of 65 inches and a standard deviation of 2.5 inches. The height of adult men is thought to have a mean of 71 inches and a standard deviation of 3 inches. In the same family, the son is 67 inches tall and the daughter is 59 inches tall. Who is taller among their gender, the son or daughter?

The son

Below is the distribution of low temperatures (in degrees F) for 52 cities in the U.S. lowtemps.jpg Based on the output, it is reasonable to model the distribution of low temperature for these cities with a normal distribution.

True