Assume that the weight of hamsters is Normally distributed with μ = 1.2 lbs and σ = 0.25 lbs. Suppose I randomly select 4 hamsters.

(a) What is the shape of the sampling distribution of the sample mean? (unknown, exactly normal, approximately normal)

(b) What is P(X < 1.14)? (Use 3 decimal places)

Given Information:  

Population mean = μ = 1.2

Population standard deviation = σ = 0.25  

Sample size n = 4

Required Information:  

P(X < 1.14) = ?

The probability of P(X < 1.14) is 0.315

Explanation:  

(a) What is the shape of the sampling distribution of the sample mean?

Since it is given that population is normally distributed then sample distribution will also be normally distributed even with a smaller sample size .

When population is not normally distributed and is very skewed then a larger sample size is required to ensure normal sample distribution according to central limit theorem.

(b) What is P(X < 1.14)?

First let us find out sample mean and standard deviation

sample mean will be same as population mean μ = 1.2

sample standard deviation =  σ/√n

where n = 4 is given

sample standard deviation =  σ/√4 =  0.125

Now we can calculate the probability using z-score

P(X < 1.14) = P(Z < (1.14 - 1.2)/0.125) = P(Z < -0.48)

From the z-table

P(Z < -0.48) = 0.3156

Therefore, the probability of P(X < 1.14) is 0.315 or 31.5%

51-50

step-by-step explanation:

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