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StatisticsQ&A LibraryThe 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.)Question

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.)

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:

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:

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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