A college has 230 full-time employees that are currently covered under the schoo

Question

A college has 230 full-time employees that are currently covered under the school's health care plan. The average out-of-pocket cost for the employees on the plan is $1,850 with a standard deviation of $520. The college is performing an audit of its health care plan and has randomly selected 30 employees to analyze their out-of-pocket costs a. Calculate the standard error of the mean b. What is the probability that the sample mean will be less than $1,800? c. What is the probability that the sample mean will be more than $1,820? d. What is the probability that the sample mean will be between $1,875 and $1,910 12 a. The standard error of the mean is (Round to two decimal places as needed) b. The probability that the sample mean will be less than 1.800 is Round to four decimal places as needed) c. The probability that the sample mean will be more than 1.820 is Round to four decimal places as needed) d. The probability that the sample mean will be between 1,875 and 1,910 is (Round to four decimal places as needed)

Explanation / Answer

Ans:

Given that

mean=1850

standard deviation=520

sample size,n=30

a)standard error of mean=520/sqrt(30)=94.94

b)

z=(1800-1850)/94.94=-0.527

P(z<-0.527)=0.2992

c)

z=(1820-1850)/94.94=-0.316

P(z>-0.316)=0.6240

d)

z(1875)=(1875-1850)/94.94=0.263

z(1910)=(1910-1850)/94.94=0.632

P(0.263<z<0.632)=P(z<0.632)-P(z<0.263)=0.7363-0.6038=0.1325

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