Question

In: Statistics and Probability

Video: The Normal Distribution 1.In the United States, the average weight of an adult male is...

Video: The Normal Distribution

1.In the United States, the average weight of an adult male is approximately 172 pounds with a standard deviation of about 30 pounds. If a man weighs 145 pounds, how many standard deviations above/below the mean is he?

A man who weighs 145 pounds is____________ standard deviations__________ the mean.

2.For this question, refer to the normal probability distribution table found here

In the United States, the average weight of an adult male is approximately 172 pounds with a standard deviation of about 30 pounds. Assuming a normal distribution, what proportion of men weigh less than 145 pounds? Express your answer as a decimal rounded to four digits after the decimal point.

3. When considering a normal distribution, proportions can be thought of as areas of regions. The areas can be found using a probability distribution table. To find the proportion of data that falls between two values, look up the appropriate two z scores in the table and      Select an answerdividesubtractmultiplyadd the values.

4. For this question, refer to the normal probability distribution table found here
In the United States, the average weight of an adult male is approximately 172 pounds with a standard deviation of about 30 pounds. Assuming a normal distribution, how much would a man weigh at the 80th percentile? Round your answer to the nearest pound.

pounds.

Solutions

Expert Solution

1) Given that the average weight of an adult male is approximately M = 172 pounds with a standard deviation of about =30 pounds. If a man weighs X= 145 pounds, the no of standard deviations above/below the mean is he is calculated by finding the Z score.

The Z score is calculated as:

A man who weighs 145 pounds is -0,90 standard deviations below the mean.

2) For this normal distribution, the probability is calculated by the Z score using an excel formula for normal distribution.

The average weight of an adult male is approximately 172 pounds with a standard deviation of about 30 pounds. Assuming a normal distribution, the proportion of men weigh less than 145 pounds P(X<145), is calculated by finding the Z score which is:

Now, P(X<145) = P(Z<-0.90) is computed using excel formula which is =NORM.S.DIST(-0.90, TRUE) this results in probability value as 0.1841.

4) In the United States, the average weight of an adult male is approximately M = 172 pounds with a standard deviation of about = 30 pounds. Assuming a normal distribution, then a man weighs at the 80th percentile is computed by finding the Z score at 80th percentile which is again computed using excel formula for normal distribution, and by using the Z score we will be able to find the man weight at 80th percentile.

The Formula used is =NORM.S.INV(0.8) this results in Z =0.8416

Now by using excel formula :

Note: Part 3 has no question it has just instructions.


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