Please answer with method or formula used.

Select a person at random at a local baseball game. Consider these events: C = person buys soda, B = person buys beer, N = person buys peanuts

Consider these probabilities: a) The probability the person buys none of the things. b) The probability the person buys exactly one of the things c) The probability the person buys all three, given that he buys at least 2. d) The probability the person buys peanut, given that he doesn’t buy beer

A) Calculate (a)-(d) assuming that ?(?) = 0.40, ?(?) = 0.60, ?(?) = 0.30, ?(? ∩ ? ∩ ?) = 0.08

B) ?(? ∪ ?) = 0.83, ?(? ∪ ?) = 0.50, ?(? ∩ ?) = 0.15 , ,

C) Calculate (a)-(d) assuming that ?(?) = 0.40, ?(?) = 0.60, ?(?) = 0.30 , and that C, B, N are independent events.

D) A pair of 6-sided die is tossed. If the sum of the two die is at least 10, you win $10. sum of the die is a number between 4 and 9, you win $5. less than 4, you win $0.
1) What are the possible winnings? 2) What is the probability for each possibility, assuming that the die are fair? 3) What is the expected winnings? 4) What is the variance of winnings?

E) Let X be the payout from the previous problem. Compute a) ?(1/?) b) c) ?(2.3? − 1.5) d) ?(2.3 − 1.5)

QUESTION 2 [20 MARKS] Information on three age groups and three salary bands in a mining company is being analyzed. First, it is summarized into a contingency table before this analysis. The table, showing the age groups, the salary bands and the number of employees per each combination of salary band and age group is shown below. Age Group Salary Band Less than 40 year 40 to 60 years More than 60 years Less than P20, 000 35 40 10 P20, 000 – P40, 000 21 30 15 More than P40, 000 16 25 8 a. Produce a probability contingency table for the data including the totals. b. If an employee is randomly chosen, what is the probability that he/she is in the 40 to 60 years age group earning between P20, 000 and P40, 000? c. If an employee is randomly chosen, what is the probability that he/she is less than 40 years of age or earning more than P40, 000? d. Given that the employee earns less than P20, 000, what is the probability that he/she is aged above 60 years (give answer to 4 decimal places)? e. If an employee is randomly chosen, what is the probability that he/she is aged 60 years and less?

Suppose that the distribution of typing speed in words per minute (wpm) for experienced typists using a new type of split keyboard can be approximated by a normal curve with mean 68 wpm and standard deviation 17 wpm.

What is the probability that a randomly selected typist's speed is at most 68 wpm?

What is the probability that a randomly selected typist's speed is less than 68 wpm?

What is the probability that a randomly selected typist's speed is between 34 and 85 wpm? (Round your answer to four decimal places.)

Would you be surprised to find a typist in this population whose speed exceeded 119 wpm? (Round your numerical value to four decimal places.)

It would  ---Select--- (be, not be) surprising to find a typist in this population whose speed exceeded 119 wpm because this probability is ________ , which is  ---Select--- (very small, very large) .

Suppose that two typists are independently selected. What is the probability that both their typing speeds exceed 102 wpm? (Round your answer to three decimal places.)

Suppose that special training is to be made available to the slowest 20% of the typists. What typing speeds would qualify individuals for this training? (Round your answer to the nearest whole number.)

People with typing speeds of  wpm and  ---Select--- (above, below) would qualify for the training.

A recent national survey found that parents read an average (mean) of 10 books per month to their children under five years old. The population standard deviation is 5. The distribution of books read per month follows the normal distribution. A random sample of 25 households revealed that the mean number of books read last month was 12. At the .01 significance level, can we conclude that parents read more than the average number of books to their children?

What is the probability of a Type II error? (Round your answer to 4 decimal places.)

8% of men are red-green colorblind. A sample of 125 men is gathered from a particular subpopulation, and 13 men in this sample are colorblind.

a. Is this statistically significant evidence that the proportion of red-green colorblind men is greater than the subpopulation than the national average with alpha = 0.05?

b. What is the maximum number of men that could have been colorblind in this sample that would lead you to fail to reject the null hypothesis?

c. Using 8% as the probability of being colorblind, find a 95% confidence interval for the number of men in a sample of 125 who are colorblind.

The number of passengers arriving at a checkout counter of an international airport follows a Poisson distribution. On average, 4 customers arrive every 5-minutes period. The probability that over any 10-minute interval, at most 5 passengers will arrive at the checkout counter is

A:- 0.1221

B:- 0.1250

C:- 0.2215

D:- 0.8088

The number of customers who enter a bank is thought to be Poisson distributed with a mean equal to 10 per hour. What are the chances that 2 or 3 customers will arrive in a 15-minute period?

A:- 0.0099

B:- 0.4703

C:- 0.0427

D:- 0.0053

Every day there is a random number of pencils in the mail. Jerry places eraser caps on each one that arrives. Jerry has enough eraser caps to cap 600 pencils. Each day, Jerry gets at least two pencils, but not more than a dozen, and he always receives an even number of pencils. Among the possible numbers of pencils Jerry might receive, all are equally likely. Moreover, different days are independent. What is the approximate probability that Jerry's amount of eraser caps will last at least three months? Assume there are 30 days in every month.

A random group of thirty customers at a local theater was interviewed regarding their movie viewing habits. The following responses were obtained for the question, “How many times during the past month did you go to the movies?” Number of movies attended 0 1 2 3 4 Number of customers 3 10 8 6 3 a. b. Find the probability that a customer selected at random went to the movies:

1) more than one time, 2) two times, 3) at least two times, 4) no more than three times.

When parking a car in a downtown parking lot, drivers pay according to the number of hours or fraction thereof. The probability distribution of the number of hours cars are parked has been estimated as follows:

A. Mean =

B. Standard Deviation =

The cost of parking is 2.25 dollars per hour. Calculate the mean and standard deviation of the amount of revenue each car generates.

A. Mean =

B. Standard Deviation =