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


Related Solutions

The number of patients needing admission each day to a hospital intensive care unit (ICU) has...
The number of patients needing admission each day to a hospital intensive care unit (ICU) has a Poisson distribution with a mean of 5.3. (a) Why might it be reasonable to expect that daily numbers of patients would have a Poisson distribution rather than any other distribution? (b) Assuming that patients only stay in the ICU for one day, what is the probability that an 8-bedded ICU will have to turn patients away on any particular day? (c) How many...
The distribution of the number of siblings for students at a large high school is skewed...
The distribution of the number of siblings for students at a large high school is skewed to the right with mean 1.8 siblings and standard deviation 0.7 sibling. A random sample of 100 students from the high school will be selected, and the mean number of siblings in the sample will be calculated. Which of the following describes the sampling distribution of the sample mean for samples of size 100 ? A Skewed to the right with standard deviation 0.7...
The table below shows the number of hours per day 11 patients suffered from headaches before...
The table below shows the number of hours per day 11 patients suffered from headaches before and after 7 weeks of soft tissue therapy. At alphaαequals= 0.01,is there enough evidence to conclude that soft tissue therapy helps to reduce the length of time patients suffer from headaches? Assume the samples are random and dependent, and the population is normally distributed. Complete parts (a) through (f). Patient Daily headache hours (before) Daily headache hours (after) 1 4.1 2.2 2 2.2 1.6...
The table below shows the number of hours per day 11 patients suffered from headaches before...
The table below shows the number of hours per day 11 patients suffered from headaches before and after 7 weeks of soft tissue therapy. At α =​0.01, is there enough evidence to conclude that soft tissue therapy helps to reduce the length of time patients suffer from​ headaches? Assume the samples are random and​ dependent, and the population is normally distributed. USE THE CRITICAL REGION METHOD Patient: 1 2 3 4 5 6 7 8 9 10 11 Daily Headache...
The table below shows the number of hours per day 11 patients suffered from headaches before...
The table below shows the number of hours per day 11 patients suffered from headaches before and after 7 weeks of soft tissue therapy. At α=​0.01,is there enough evidence to conclude that soft tissue therapy helps to reduce the length of time patients suffer from​headaches? Assume the samples are random and​ dependent, and the population is normally distributed. Complete parts​ (a) through​ (f). Patient Daily headache hours (before) Daily headache hours (after) 1 2.6 1.8 2 2.1 1.6 3 1.7...
Best Electronics offers a “no hassle” returns policy. The number of items returned per day follows...
Best Electronics offers a “no hassle” returns policy. The number of items returned per day follows the normal distribution. The mean number of customer returns is 8.2 per day and the standard deviation is 1.60 per day. Refer to the table in Appendix B.1.   a. In what percentage of the days 6 or fewer customers returning items? (Round z-score computation to 2 decimal places and the final answer to 2 decimal places.) Percentage            % b. In what percentage of...
Best Electronics offers a “no hassle” returns policy. The number of items returned per day follows...
Best Electronics offers a “no hassle” returns policy. The number of items returned per day follows the normal distribution. The mean number of customer returns is 9.6 per day and the standard deviation is 2.30 per day. Refer to the table in Appendix B.1.   a. In what percentage of the days 6 or fewer customers returning items? (Round z-score computation to 2 decimal places and the final answer to 2 decimal places.) Percentage            % b. In what percentage of...
Question 7 Many populations which auditors audit are skewed. There is a large number of smaller...
Question 7 Many populations which auditors audit are skewed. There is a large number of smaller transactions, but the number of larger transactions tails off, making the population look like an F distribution. Required: a. Is it appropriate to perform statistical sampling from such a population? b. Why is it appropriate, or why it is not appropriate, to perform statistical sampling from such a population? c. If the auditor uses parametric statistics (based on a normal distribution), will those statistics...
Table 1 Number of Workers Sheets of Metal per day (in pounds) 0 0 1 10...
Table 1 Number of Workers Sheets of Metal per day (in pounds) 0 0 1 10 2 22 3 32 4 40 5 46 6 50 If the average total cost of producing 12 dozen sheets of metal is $6, and the average total cost of producing 13 dozen muffins is $7, then how much is the marginal cost of producing the 13thdozen metal sheet? Explain the formulas you use and show your math. Assume that Joe’s fixed cost are...
Table 1 Number of Workers Sheets of Metal per day (in pounds) 0 0 1 10...
Table 1 Number of Workers Sheets of Metal per day (in pounds) 0 0 1 10 2 22 3 32 4 40 5 46 6 50 Assume that Joe’s fixed cost are $2,000, and his variable cost per worker is $400. Calculate the cost data for Joe’s roll forming company using Table 2 below. For each column, explain what is happening to Joe’s costs. Draw one graph showing Joe’s TC. Draw another graph showing Joe’s AFC, AVC, ATC, and MC.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT