Statistics 561: Mean,Median,Standard deviation, Distribution

1. Below is the result of a statistical study on a small sample based on an hourly wage rate:

Wage rate ($) Frequency
5 up to 10 3
10 up to 15 0
15 up to 20 10
20 up to 25 5
25 up to 30 12

a. Determine the mean of the hourly wage rates

Xbar =

b. What is the mode of the wage rate distribution?

Mode =

c. Based on the class limits, what percentage of this sample makes at least $20.00 hourly wage?

Answer:

2. We picked seven households at random and found that they should be investigated by the Wildlife Society because too many creatures live there. The list below gives number of creatures found in each of those households: 6, 5, 8, 9, 7, 8, 9

a. Find the standard deviation of creatures occupying these households?

b. What is the median?

3. We looked at the U.S. population that own homes: 30% own a house with only one garage, 40% own a garage and additional parking space, 20% park their car on a street, and 10% have only one parking space.

a. What is a probability that household has a garage?

b. What is a probability that two homes, selected randomly, would have a garage?

c. What is a probability that household has a garage or a parking space?

d. If we select 5 households at random, what is the probability that at least three of them have to park their cars on the street?

4. The famous restaurant owner noticed that in the past twenty years his steak supply shows a normal distribution in weight. Average weight was 10.0 ounces with a standard deviation of 0.3 ounces.

a. What is the probability that a customer gets a steak that weighs at least 9.6 ounces?

b. If a customer gets a steak that falls in the upper 70% of the weight distribution, what is the minimum weight of his steak?

c. What is a probability that a sample of 16 steaks would have the mean value greater than 10.1 ounces?

d. The prime rib is also on the menu, but it is a new item and only 300 of them were sold up to date. We want to help the restaurant owner with his statistics so he can make some claims about this new dish. We took a sample of 25 prime ribs and the sample showed the mean weight of 14.5 ounces with the standard deviation of .2 ounces. Using the level of significance equal to 5% ( = .05), what is the confidence interval for the mean weight of the prime rib?