The annual per capita consumption of fresh bananas​ (in pounds) in the United States can be approximiated by the normal​ distribution, with a mean of 10.4 pounds and a standard deviation of 1 pound. Answer the following questions about the specified normal distribution.(a) What is the smallest annual per capita consumption of bananas that can be in the top 10% of​ consumptions?(b) b) What is the largest annual per capita consumption of bananas that can be in the bottom 5% of​ consumption?(a) The smallest annual per captita consumption of bananas that can be in the top 10​% of consumptions is ______ pounds.  (Round to one decimal place as​ needed.)(b) The largest annual per capita consumption of bananas that can be in the bottom 5% of consumptions is_____  pounds. ​ (Round to one decimal place as​ needed.)

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Asked Mar 5, 2019
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The annual per capita consumption of fresh bananas (in pounds) in the United States can be approximiated by the normal distribution, with a mean of 10.4 pounds and a standard deviation of 1 pound. Answer the following questions about the specified normal distribution.

(a) What is the smallest annual per capita consumption of bananas that can be in the top 10% of consumptions?

(b) b) What is the largest annual per capita consumption of bananas that can be in the bottom 5% of consumption?

(a) The smallest annual per captita consumption of bananas that can be in the top 10% of consumptions is ______ pounds.  (Round to one decimal place as needed.)

(b) The largest annual per capita consumption of bananas that can be in the bottom 5% of consumptions is_____  pounds. (Round to one decimal place as needed.)

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Expert Answer

Step 1

Standard normal distribution:

The standard normal distribution is a special case of normal distribution. The standard normal distribution will have mean 0 and standard deviation 1. If a random variable y follows normal distribution with mean (m) and standard deviation (s), then the standard normal variable z will be as given below:

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Step 2

Find the smallest annual per capita consumption of bananas that can be in the top 10% of consumptions:

Consider the variable annual per capita consumption of fresh bananas be denoted by y. It is given that the annual per capita consumption of fresh bananas are normally distributed.

The mean and standard deviation of annual per capita consumption of fresh bananas is y-bar = 10.4 pounds and s(y) = 1.0 pounds, respectively.

The given requirement is a annual per capita consumption of bananas should be in the top 10% of consumptions. That is, P(Z > z) = 0.1.

The smallest annual per capita consumption of bananas that can be in the top 10% of consumptions is obtained as 11.68 from the calculation given below:

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Step 3

Find the largest annual per capita consumption of bananas that can be in the bottom 5% of consumptions:

The given requirement is a annual per capita consumption of bananas should be in the bottom 5% of consumptions. That is, P(Z < ...

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