Solve using Excel & Minitab (Do not use formula)

The following questions are from probability and statistics questions. The questions were previously solved by our statistic experts using MINITAB; in case you are a student looking for help with similar questions, then you can contact us so that we may provide similar services under our do MyMathLab homework so that we can provide you similar solutions, or solutions with similar questions, either using Excel data analysis tools , or by using the latest Minitab application software. The solutions to each question are attached for you confirmation.

1. A die is tossed 3 times. What is the probability of
   (a) No fives turning up?
   (b) 1 five?
   (c) 3 fives?
   Probability Solution for Question 1
   Outut for Question 1:
   Probability Density Function

Binomial with n = 3 and p = 0.17

x P( X = x )
0 0.571787
Probability Density Function
Binomial with n = 3 and p = 0.17
x P( X = x )
1 0.351339
Probability Density Function
Binomial with n = 3 and p = 0.17
x P( X = x )
3 0.004913

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?

   Question 2
   probability of 4 recoveries
   Probability Density Function
   Binomial with n = 6 and p = 0.25
   x P( X = x )
   4 0.0329590

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.)

Question 3
Probability of atleast 3 Boys
Cumulative Distribution Function
Binomial with n = 6 and p = 0.5219
x P( X ≤ x )
2 0.303638
P(x <= 3) = 1-0.3036 = 0.6957

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?

   Question 4

   a) Probability of not more than 2
   Cumulative Distribution Function
   Binomial with n = 10 and p = 0.12
   x P( X ≤ x )
   2 0.891318

b) probability of at least 2 = 1-P(x <= 1)
Cumulative Distribution Function
Binomial with n = 10 and p = 0.12
x P( X ≤ x )
1 0.658275
p(x>=2) = 1-0.6583 = 0.3417

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.

   Question 6

   exactly 3 errors.
   Results for: Q6.MTW
   Probability Density Function
   Poisson with mean = 0.4
   x P( X = x )
   3 0.0071501

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.

Question 7

At most 3 calls
P (X <= 3)
Cumulative Distribution Function
Poisson with mean = 3
x P( X ≤ x )
3 0.647232
b At Least 3 Calls = 1-P(X<=2)
Cumulative Distribution Function
Poisson with mean = 3
x P( X ≤ x )
2 0.423190
p(X>=3) = 1-0.42319 = 0.5768
c Probability of five or More calls
= 1- p(X<=4)
Cumulative Distribution Function
Poisson with mean = 3
x P( X ≤ x )
4 0.815263
p(x>=5) = 1-0.815263 = 0.1847

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

A solution to this probability question has been provided by our experts, you may contact us if you need help with this question.

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

You can solve this question using either Excel data analysis tools, or Minitab, when you choose to use Excel, then use the function =NORM.S.DIST(1.11,TRUE) = 0.8665, which gives you the area to the left, to find the area to the right = 1-0.8665 = 0.1335

11. Find the area left of z = -1.93
    You can also apply similar tactics as above to solve this question.
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.

This question has been solved in many of our questions under our myMathlab homework help services.

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?