Assume X ~ ? (10, 4) where ? implies unknown.

1. What is the (approximate) distribution of if the sample size is 100? Briefly discuss the theorem underlying your answer.

2. What happens to the variance of as the sample size increases? Draw a diagram and explain.

3. What two values of (symmetric around the population mean) contain a) 75% and b) 95% of the distribution? Draw a diagram. Relate your answer to b) to the empirical rule.

Scores of an IQ test have a​ bell-shaped distribution with a mean of

100

and a standard deviation of

13

Use the empirical rule to determine the following.

​(a) What percentage of people has an IQ score between

87

and

113​?

​(b) What percentage of people has an IQ score less than

74

or greater than

126​?

​(c) What percentage of people has an IQ score greater than

126​?

Current activity in the hospital industry shows that hospitals are consolidating to form multihospital systems. Based upon your reading in the text, what do empirical studies indicate concerning cost savings of multihospital systems over single hospital systems? Why are multihospital systems expected to be cost saving? Why would we continue to see multihospital systems forming even if cost savings is not as evident as expected?

The shelf life of a battery produced by one major company is known to be normally distributed, with a mean life of 3.2 years and a standard deviation of 0.5 years. Using the expanded empirical rule, what is the probability in decimal form that a randomly chosen battery will

(a) last fewer than 3.535 years?
Answer:

(b) last between 2.7 and 3.7 years?
Answer:

(c) last more than 1.7 years?
Answer:

1. Use the following data

2. X                      f(X)

   0	0.10
   1	0.15
   2	0.30
   3	0.20
   4	0.15
   5	0.10

3. Graph the probability distribution of X
4. Calculate ?_" and ?$.
5. Calculate the interval (?_" ± 2?_"). Superimpose this interval on the graph of the probability distribution of X. Also, calculate the interval (?_" ± ?_"). What proportion of the measurements will fall within these intervals? Does this result agree with Chebyshev’s Theorem? The Empirical Rule?

Let X1, X2, ..., X25 be a sample from Exp(10) distribution.

1- What is the expected value of its sample variance?

2- Write an R code that generates hundred thousand repetitions of the sample variance and create a

histogram of the resulting vector via standard hist function.

3- Use the density function to get a sample variance empirical pdf and add it to the plot obtained in part (2).

Scores of an IQ test have a​ bell-shaped distribution with a mean of 100 and a standard deviation of 13.

Use the empirical rule to determine the following.

​(a) What percentage of people has an IQ score between 87 and 113​?

​(b) What percentage of people has an IQ score less than 87 or greater than 113​?

​(c) What percentage of people has an IQ score greater than 139?

Scores of an IQ test have a​ bell-shaped distribution with a mean of 100 and a standard deviation of 18. Use the empirical rule to determine the following. ​(a) What percentage of people has an IQ score between 64 and 136​? ​(b) What percentage of people has an IQ score less than 64 or greater than 136​? ​(c) What percentage of people has an IQ score greater than 154​?

Scores of an IQ test have a​ bell-shaped distribution with a mean of 100 and a standard deviation of 13. Use the empirical rule to determine the following. ​

(a) What percentage of people has an IQ score between 61 and 139?

​(b) What percentage of people has an IQ score less than 74 or greater than 126? ​

(c) What percentage of people has an IQ score greater than 113? ​

Scores of an IQ test have a​ bell-shaped distribution with a mean of 100 and a standard deviation of 18. Use the empirical rule to determine the following.

​(a) What percentage of people has an IQ score between 82 and 118​?

​(b) What percentage of people has an IQ score less than 64 or greater than 136​?

​(c) What percentage of people has an IQ score greater than 118​?