Question

Question 22 4 pts 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. Does the Central Limit Theorem apply to this problem? No Yes, since np and nq are both at least 15 Yes, since n is at least 30.

Answer 1

Answer Date: 26/06/2020 22) The central limit theorem does apply to this problem due to the sample size is at least 36 which is 100. The option (1) is incorrect due to the central limit theorem does apply. The option (2) is incorrect because to the np and nq both are at least 15 condition is incorrect instead of the correct condition of np and nq 10 but it also incorrect due to it is used for sampling distribution of sample proportion instead of sampling distribution o: sample mean. The answer option is 3 Part 2 The probability is that the mean in the sample exceeded 24 days is,

First, compute the mean and standard deviation for sample mean then find probability. The mean for the sampling distribution of sample means is, μα = μ = 20 Standard deviation of the sampling distribution of sample mean is, O 8 V100 = 0.80 The probability is that the mean in the sample exceeded 24 days is, First, compute the z score then find probability based on standard normal table.

For i = 24 converts to I-Us Z = 24 - 20 0.80 = 5.00 From the standard normal distribution table, the associated probability is 1.0000. Since find the area to the right, so subtract from 1 to get, p(z > 5.00) = 1-p(z< 5.00) = 1-1.0000 = 0.0000 The probability is that the mean in the sample exceeded 24 days is approximately 0. The answer option is 2

Part 3 The sample size is, First, compute the z-critical value then find the sample size. The Z-critical value is, From the standard normal table, the z-critical value at 90% confidence is 1.645. The information represent E = 0.02, p = 0.10 and ze = 1.645 for finding sample size. n= Zc E xp(1-P) 1.645 = (10.02 x 0.10(1-0.10) 0.02 = 608.86 = 609 The sample size is 609. The answer option is 2