The standard deviation of the lengths of hospital stay on the intervention ward is

8.2 days.

Complete parts (a) through (c) below.

a. For the variable "length of hospital stay," determine the sampling distribution of the sample mean for samples of

87

patients.

The standard deviation of the sample mean is

sigma Subscript x overbar

equals0.88

days.

(Round to four decimal places as needed.)

b. The distribution of the length of hospital stay is right skewed. Does this invalidate your result in part (a)? Explain your answer.

A.

Yes, because

x overbar

is only normally distributed if x is normally distributed.

B.

No, because the sample sizes are sufficiently large that

x overbar

will be approximately normally distributed, regardless of the distribution of x.

C.

No, because if

x overbar

is normally distributed, then x must be normally distributed.

D.

Yes, because the sample sizes are not sufficiently large that

x overbar

will be approximately normally distributed, regardless of the distribution of x.

c. Obtain the probability that the sampling error made in estimating the population mean length of stay by the mean length of stay of a sample of

87

patients will be at most 2 days.

The probability is approximately

nothing

.

(Round to three decimal places as needed.)