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Five Statistics Probability Questions

1) An oil change shop advertised to change oil within 20 minutes. Based on the data collected on five days of work, what is the probability that oil change will take less than 20 minutes? Based on the data, do you think the business claim is valid? Explain why or why not. If not, what advertising claim could you make based upon these results?

Class | Interval | Frequency
6 | up to 10 minutes | 24
10 | up to 15 minutes | 111
15 | up to 20 minutes | 405
20 | up to 25 minutes | 36
25 | or more minutes | 24

Note: The use of "up to" is a technique of avoiding overlap in class intervals or categories. So, a time of ten minutes would be placed in the second class interval (10 up to 15 minutes) rather than the first interval.

2) Here is an application. From a review of the literature, I find that the mean number of widgets produced in an eight hour shift is 170 with a standard deviation of 14 minutes. What is your chance of your factory producing more than 180 widgets in a shift? You would use the z score formula, so 180-170/14. Z would equal .71. Using the standard normal table, I find the probability that associated with z = .71 is .2611. Thus, the chance of producing more than 180 widgets in a shift is .2389, or .5 - .2611. (Using a cumulative standard normal table, I would find the p for z = .71, which is .7611. I would then use the complement, or 1-.7611 to find the probability of .2389). So, you have about a 24% chance.

What would be my probability of producing less than 160 widgets in a shift?

3) In each of the following cases, indicate whether classical, empirical, or subjective probability is used.

a. A baseball player gets a hit in 30 out of 100 times at bat. The probability is .3 that he gets a hit in his next at bat.
b. A seven-member committee of students is formed to study environmental issues. What is the likelihood that any one of the seven is chosen as the spokesperson?
c. You purchase one of 25 million tickets sold for MegaMillions. What is the likelihood you will win the jackpot?
d. The probability of an earthquake in northern California in the next 10 years above 5.0 on the Richter Scale is .80.

4) At my workplace, probability is the essential tool the inventory personnel applies in handling inventory. The first thing we do is collect the data and then we evaluate it. By thoroughly evaluating the data, allows us to figure out what products are possibly needed at once. Although we have a profound method in place, considering organizational changes and the market, we cannot always assume that the method is going to continuously work over a long period of time. We have to go back and collect additional data and evaluate it to determine if the plan of action is benefiting the company. If it is not effective, then we have to figure out why and come up with new methods that will better suit the present needs of the company. Also, the inventory personnel can use probability to a certain extent to estimate how specific adjustments to the plan may affect the company's profit.

What approach to probability is this example?

) The three approaches to assigning probabilities are: classical, relative frequency, and subjective.

What are the differences in these three approaches? Could you explain each, and provide an example?

Solution Preview

As per the data, the number of times the oil change has taken 20 minutes or less time=24+111+405=540. Since the total frequency = 540+36+24=600. Hence, the probability that the oil change will take less than 20 minutes=540/600=0.9. It seems that the above probability value is too high. This means it is unlikely that the oil change will happen in less than 20 minutes. The claim is not valid. The problem here is that the size of data set is too small and by taking the data for just one day, we still do not know if the shop is consistent over a certain period of time. Hence, we ...

Solution Summary

The solution gives detailed steps on solving 5 probability question in the form of both concept and computations.