Question

In: Statistics and Probability

10) The number of patients admitted per day to a large hospital's ICU follows a skewed...

10) The number of patients admitted per day to a large hospital's ICU follows a skewed right distribution with a mean of 20 and a standard deviation of 8. Suppose a sample of 100 days was collected over the past year and the average number of patients admitted per day was calculated.

a) Which of the following statements about the sampling distribution of the sample mean is correct?

-It is a skewed right distribution with a mean of 20 and a standard deviation of .8.

-It is approximately normally distributed with a mean of 20 and a standard deviation of .8.

-It is approximately normally distributed with a mean of 20 and a standard deviation of 8.

-It is a skewed right distribution with a mean of 20 and a standard deviation of 8.

b) Does the Central Limit Theorem apply to this problem?

-Yes, since np and nq are both at least 15

-No

-Yes, since n is at least 30.

c) What is the probability that the mean in the sample exceeded 24 days?

-Approximately 1

-.1915

-Approximately 0

-.3085

Solutions

Expert Solution

Solution :

Given that,

mean = = 20

standard deviation = = 8

a) n = 100

= = 20

= / n = 8 / 100 = 0.8

It is approximately normally distributed with a mean of 20 and a standard deviation of .8

b) Yes, since n is at least 30

c) P( > 24 ) = 1 - P( < 24)

= 1 - P[( - ) / < (24 - 20) / 0.8 ]

= 1 - P(z < 5.0)

= 1 - 1

= 0

Approximately 0

orchestra answered 1 year ago

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