The weights of gala apples follow a Normal distribution with a mean of 140 grams and a standard deviation of 12 grams. The owner of an apple orchard randomly selects 5 apples from the harvest and records the mean weight. What is the shape of the distribution of the sample mean for all possible random samples of size 5 from this population?

The shape is approximately normal, with mean of 140 grams and standard deviation of 5.37 grams.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean and standard deviation , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean and standard deviation .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean and standard deviation

What is the shape of the distribution of the sample mean for all possible random samples of size 5 from this population?

By the Central Limit Theorem, the shape is approximately normal.

Mean is

Standard deviation is

The shape is approximately normal, with mean of 140 grams and standard deviation of 5.37 grams.

step-by-step explanation:

first, eliminate the parenthesis:

3

x

+

2

−

4

x

second, group like terms:

3

x

−

4

x

+

2

third, combine like terms:

(

3

−

4

)

x

+

2

→

−

1

x

+

2

→

−

x

+

2

1: -2 3/4, -2 1/2, -14, 0, 3, 8 1/3

2: -4, -3, -2 1/2, -2 1/4, 3 1/4,

step-by-step explanation: