# Solve using Excel and Minitab: the probability that of 6 randomly selected patients, 4 will recover

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Solve using Excel & Minitab (Do not use formula)

1. A die is tossed 3 times. What is the probability of

(a) No fives turning up?

(b) 1 five?

(c) 3 fives?

2. Hospital records show that of patients suffering from a certain disease, 75% die of it. What is the probability that of 6 randomly selected patients, 4 will recover?

3. The ratio of boys to girls at birth in Singapore is quite high at 1.09:1.

What proportion of Singapore families with exactly 6 children will have at least 3 boys? (Ignore the probability of multiple births.)

4. A manufacturer of metal pistons finds that on the average, 12% of his pistons are rejected because they are either oversize or undersize. What is the probability that a batch of 10 pistons will contain

(a) no more than 2 rejects? (b) at least 2 rejects?

5. A die is rolled 240 times. Find the mean, variance and standard deviation for the number of 3s that will be rolled?

6. If there are 200 typographical errors randomly distributed in a 500 page manuscript, find the probability that a given page contains exactly 3 errors.

7. A sales form receives on the average of 3 calls per hour on its toll-free number. For any given hour, find the probability that it will receive a. At most 3 calls; b. At least 3 calls; and c. Five or more calls.

8. A life insurance salesman sells on the average 3 life insurance policies per week. Calculate the probability that in a given week he will sell

1. Some policies
2. 2 or more policies but less than 5 policies.
3. Assuming that there are 5 working days per week, what is the probability that in a given day he will sell one policy?

9. Twenty sheets of aluminum alloy were examined for surface flaws. The frequency of the number of sheets with a given number of flaws per sheet was as follows:

 Number of flaws Frequency 0 4 1 3 2 5 3 2 4 4 5 1 6 1

What is the probability of finding a sheet chosen at random which contains 3 or more surface flaws?

10. Find the area right of z=1.11

11. Find the area left of z = -1.93

12. Find the area between -/+ 1, 2, 3, 4, 5, 6, standard deviations.

13. Find the z value such that the area under the normal distribution curve between 0 and the z value is 0.2123

14. A study on recycling shows that in a certain city, each household accumulates an average of 14 pounds of newspaper each month to be recycled. The standard deviation is 2 pounds. If a household is selected at random, find the probability it will accumulate the following:

a. Between 13 and 17 pounds of newspaper for a month.

b. More than 16.2 pounds of newspaper for one month.

15. A standardized achievement test has a mean of 50 and a standard deviation of 10. The scores are normally distributed. If the test is administered to 800 selected people, approximately how many will score between 48 and 62?

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