Answer:
The mean of the sampling distribution is 86
The standard deviation of the sampling distribution is 2
The mean of the sampling distribution is 71
The standard deviation of the sampling distribution is 1
B) The distribution is approximately normal.
Therefore, the probability that the sample mean is greater than 73 = 0.0228
The probability that the sample mean is less than or equal to 69 is 0.0228
Thus, the probability that the sample mean is between 69.8 and 72 is 0.8181.
Step-by-step explanation:
We are to determine the and from the given parameters of a population and sample size.
Given that :
population mean = 86
population standard deviation = 16
sample size n = 64
From the central limit theorem's knowledge, we know that as the sample distribution approximates a normal distribution, the sample size gets larger. Thus, the mean of the sampling distribution is equal to the population mean
∴
= = 86
The standard deviation of the sampling distribution can be computed by using the formula:
∴
The mean of the sampling distribution is 86
The standard deviation of the sampling distribution is 2
Suppose a simple random sample of size n = 36 is obtained from a population with mu = 71 and sigma = 6.
i.e
sample size n = 36
population mean = 71
standard deviation = 6
From the central limit theorem's knowledge, we know that as the sample distribution approximates a normal distribution, the sample size gets larger. Thus, the mean of the sampling distribution is equal to the population mean
∴
= = 71
The standard deviation of this sampling distribution can be estimated as :
∴
The mean of the sampling distribution is 71
The standard deviation of the sampling distribution is 1
A)
The correct option from the given question is:
B) The distribution is approximately normal.
B) What is P (xbar > 73)?
i.e
Using the Excel Function ( =NORMDIST(2) )
Therefore, the probability that the sample mean is greater than 73 = 0.0228
C) What is P (xbar ≤ 69)?
i.e
Using the EXCEL FUNCTION ( = NORMSDIST (-2) )
The probability that the sample mean is less than or equal to 69 is 0.0228
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