Suppose students' ages follow a skewed right distribution with a mean of 24 years old and a standard deviation of 3 years. If we randomly sample 350 students, which of the following statements about the sampling distribution of the sample mean age is incorrect?

a. The shape of the sampling distribution is approximately normal.

b. The mean of the sampling distribution is approximately 24-years old.

c. The standard deviation of the sampling distribution is equal to 5 years.

d. All of the above statements are correct.

Question

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Mathematics

17 May, 05:11

Suppose students' ages follow a skewed right distribution with a mean of 24 years old and a standard deviation of 3 years. If we randomly sample 350 students, which of the following statements about the sampling distribution of the sample mean age is incorrect?

a. The shape of the sampling distribution is approximately normal.

b. The mean of the sampling distribution is approximately 24-years old.

c. The standard deviation of the sampling distribution is equal to 5 years.

d. All of the above statements are correct.

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Answers (1)

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Ashlee Rose · Answer 1

Answer: Option 'c' is correct.

Step-by-step explanation:

Since we have given that

Mean of students' age = 24 years

Standard deviation of students' age = 3 years

Sample size = number of students = 350

So, according to options,

a. The shape of the sampling distribution is approximately normal.

It is true as n >30, we will use normal.

b. The mean of the sampling distribution is approximately 24-years old.

It is true as it is given.

c. The standard deviation of the sampling distribution is equal to 5 years.

It is not true as it is given 3 years.

Hence, Option 'c' is correct.