Question

(AP Statistics - Will give brainliest) The weight of apples at the grocery store follows a Normal distribution with a mean of μ = 5 ounces and a standard deviation of σ = 1 ounce. Suppose we pick nine apples at random from the basket and find their total weight, W. Which of the following statements describes the random variable W?
The random variable W is Normal, with a mean of five ounces and a standard deviation of one ounce.
The random variable W is Normal, with a mean of 45 ounces and a standard deviation of three ounces.
The random variable W is Normal, with a mean of five ounces and a standard deviation of three ounces.
The random variable W is binomial, with a mean of 45 ounces and a standard deviation of nine ounces.
The random variable W is binomial, with a mean of five ounces and a standard deviation of nine ounces.

Answer 1

The random variable W is Normal, with a mean of 45 ounces and a standard deviation of three ounces.

How to describe the random variable?

The given parameters are:

• Sample size, n = 9
• Population mean, μ = 5 ounces
• Standard deviation, σ = 1 ounce

The mean of the 9 apples is:

μ = 5 ounces * 9

This gives

μ = 45 ounces

The variance of the 9 apples is:

σ² = 1 ounces * 9

This gives

σ² = 9 ounces

Take the square root of both sides, to calculate the standard deviation.

σ = 3 ounces

Since, the variable W is normal; the description of the variable W is (b)

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