Standard Deviation

1

. A set of final exam scores in an organic chemistry course was found to be normally distributed, with a mean of 7

3

and a standard deviation of 8.
What is the probability of getting a score between 65 and 89 on this exam?

2

. Suppose that the average weekly earnings for employees in general automotive repair shops is $

45

0, and that the standard deviation for the weekly earnings for such employees is $50. A sample of

100

such employees is selected at random.
Find the

 

standard deviation of the sampling distribution of the means of average weekly earnings for samples of size 100.

3. The average hourly wage of workers at a fast food restaurant is $6.50/hr with a standard deviation of $0.45. Assume that the distribution is normally distributed. If a worker at this fast food restaurant is selected at random, what is the probability that the worker earns more than $6.

75

? 4 decimals

4. The mean weight of loads of coal placed in train cars by a loading machine is 43.0 tons with a standard deviation of 8.0 tons. Assuming that the weight of loads placed in the train cars by this loader are normally distributed, if a random sample of 9 loads is chosen for a weight check, find the probability that the mean weight of those loads is more than

40

.

60

tons.

 

5. A study was recently done that emphasized the problem we all face with drinking and driving. Five hundred accidents that occurred on a Saturday night were analyzed. Two items noted were the number of vehicles involved and whether alcohol played a role in the accident. The numbers are shown below:

 

                                                            Number of Vehicles Involved

 

 

 

Did alcohol play a role?	1	2	3
Yes	60	110	30	200
No	40	215	45	300
100	325	75

Given that alcohol was not involved, what proportion of the accidents involved a single vehicle