Question

A head librarian for a large city is looking at the overdue fees per user system-wide to determine if the library should extend its lending period. The average library user has $19.67 in fees, with a standard deviation of $7.02. The data is normally distributed and a sample of 72 library users is selected at random from the population. Select the expected mean and standard deviation of the sampling distribution from the options below.
a. σi= $7.02
b. σi= $0.10
c. σ = $0.83
d. µi= $0.27
e. µi= $2.80

Answer 1

Answer:

mean of the sample μ₁ = $0.27

Standard deviation of the sample σ₁ = $0.83

Step-by-step explanation:

Step(i):-

given mean of the population 'μ' = $19.67

Mean of the sample

                            $= \frac{mean}{n} = \frac{19.67}{72} = 0.27$

Mean of the sample  μ₁ = 0.27

Step(ii):-

Given standard deviation of the  population  (σ) =  $7.02

Standard deviation of sample

                             $= \frac{mean}{\sqrt{n} } = \frac{7.02}{\sqrt{72} } = 0.827$

Standard deviation of sample = 0.827≅ 0.83

Final answer:-

mean of the sample μ₁ = $0.27

Standard deviation of the sample σ₁ = $0.83