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In: Statistics and Probability

NORMAL DISTRIBUTION 1. 1A. Which of the following statements are TRUE about the Normal Distribution? Check...

NORMAL DISTRIBUTION

1A.

Which of the following statements are TRUE about the Normal Distribution? Check all that apply.
The distribution is symmetric with a single peak. 50% of the data values lie at or above the mean. Data values are spread evenly around the mean. The graph of the Normal Distribution is bell-shaped, with tapering tails that never actually touch the horizontal axis. The mean, median and mode are all equal and occur at the center of the distribution. About 95% of all data values lie within 1 standard deviation of the mean. Data values farther from the mean are less common than data values closer to the mean. 1B. Fill in the blanks. The depth of the snow in my yard is normally distributed, with a mean of 2.5 inches and a standard deviation of 0.25 inches. What value is one standard deviation below the mean? inches What value is one standard deviation above the mean? inches What is the probability that a randomly chosen location will have a snow depth between 2.25 and 2.75 inches? percent 1C. Use the Empirical Rule to answer the questions below: The distribution of weights for newborn babies is approximately normally distributed with a mean of 7.5 pounds and a standard deviation of 0.7 pounds. 1. What percent of newborn babies weigh more than 8.2 pounds? % 2. The middle 95% of newborn babies weigh between and pounds. 3. What percent of newborn babies weigh less than 6.1 pounds? % 4. Approximately 50% of newborn babies weigh more than pounds. 5. What percent of newborn babies weigh between 6.8 and 9.6 pounds? % 1D. The physical plant at the main campus of a large state university recieves daily requests to replace florecent lightbulbs. The distribution of the number of daily requests is bell-shaped and has a mean of 59 and a standard deviation of 6. Using the 68-95-99.7 rule, what is the approximate percentage of lightbulb replacement requests numbering between 59 and 71? Do not enter the percent symbol. ans = %

Which of the following statements are TRUE about the Normal Distribution? Check all that apply.

The distribution is symmetric with a single peak.
50% of the data values lie at or above the mean.
Data values are spread evenly around the mean.
The graph of the Normal Distribution is bell-shaped, with tapering tails that never actually touch the horizontal axis.
The mean, median and mode are all equal and occur at the center of the distribution.
About 95% of all data values lie within 1 standard deviation of the mean.
Data values farther from the mean are less common than data values closer to the mean.

1B.

Fill in the blanks.

The depth of the snow in my yard is normally distributed, with a mean of 2.5 inches and a standard deviation of 0.25 inches.

What value is one standard deviation below the mean?  inches

What value is one standard deviation above the mean?  inches

What is the probability that a randomly chosen location will have a snow depth between 2.25 and 2.75 inches?  percent

1C.

Use the Empirical Rule to answer the questions below:

The distribution of weights for newborn babies is approximately normally distributed with a mean of 7.5 pounds and a standard deviation of 0.7 pounds.

1. What percent of newborn babies weigh more than 8.2 pounds? %

2. The middle 95% of newborn babies weigh between and pounds.

3. What percent of newborn babies weigh less than 6.1 pounds? %

4. Approximately 50% of newborn babies weigh more than pounds.

5. What percent of newborn babies weigh between 6.8 and 9.6 pounds? %

1D.

The physical plant at the main campus of a large state university recieves daily requests to replace florecent lightbulbs. The distribution of the number of daily requests is bell-shaped and has a mean of 59 and a standard deviation of 6. Using the 68-95-99.7 rule, what is the approximate percentage of lightbulb replacement requests numbering between 59 and 71?

Do not enter the percent symbol.
ans = %

Solutions

Expert Solution

Solution:

1. A. Which of the following statements are TRUE about the Normal Distribution? Check all that apply

Answer:

The distribution is symmetric with a single peak.

Data values are spread evenly around the mean.

The graph of the Normal Distribution is bell-shaped, with tapering tails that never actually touch the horizontal axis.

The mean, median, and mode are all equal and occur at the center of the distribution.

Data values farther from the mean are less common than data values closer to the mean.

1. B

Fill in the blanks.

The depth of the snow in my yard is normally distributed, with a mean of 2.5 inches and a standard deviation of 0.25 inches.

What value is one standard deviation below the mean?

Answer:

inches
What value is one standard deviation above the mean?

Answer:

What is the probability that a randomly chosen location will have a snow depth between 2.25 and 2.75 inches?

Answer:

1C. Use the Empirical Rule to answer the questions below:

The distribution of weights for newborn babies is approximately normally distributed with a mean of 7.5 pounds and a standard deviation of 0.7 pounds.

1. What percent of newborn babies weigh more than 8.2 pounds?

Answer: 16%

2. The middle 95% of newborn babies weigh between and pounds.

Answer: The middle 95% of newborn babies weigh between 6.1 and 8.9 pounds.

3. What percent of newborn babies weigh less than 6.1 pounds?

Answer: 2.5%

4. Approximately 50% of newborn babies weigh more than pounds.

Answer: Approximately 50% of newborn babies weigh more than 7.5 pounds.

5. What percent of newborn babies weigh between 6.8 and 9.6 pounds?

Answer: 83.85%

1D. The physical plant at the main campus of a large state university receives daily requests to replace fluorescent lightbulbs. The distribution of the number of daily requests is bell-shaped and has a mean of 59 and a standard deviation of 6. Using the 68-95-99.7 rule, what is the approximate percentage of lightbulb replacement requests numbering between 59 and 71?

and: 47.5%

orchestra answered 1 year ago

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