Suppose every 10 times you cast your line into a lake you successfully get 3 fish. Assume you cast your line 100 times.

a) What is the probability of successfully catching exactly two fish in this experiment?

b) Calculate or approximate the probability that the number of fish you catch at least 5.

A particular magazine identified the top accounting firms in 15 geographic regions across a certain country. Even though all 15 regions reported growth in the past year, region A and region B reported the highest combined growths, with 23 % and 19%, respectively. A characteristic description of the accounting firms in these regions included the number of partners in the firm. The accompanying table contains data on the number of partners.

Number of partners data

a) What is the F stat test statistic?

b) What is the critical value?

c) What is the P - Value?

A particular magazine identified the top accounting firms in 15 geographic regions across a certain country. Even though all 15 regions reported growth in the past year, region A and region B reported the highest combined growths, with 23 % and 19%, respectively. A characteristic description of the accounting firms in these regions included the number of partners in the firm. The accompanying table contains data on the number of partners.

Number of partners data

a) What is the F stat test statistic?

b) What is the critical value?

c) What is the P - Value?

Poker hands with ranking. Consider a regular deck of 52 cards as usual with 5 cards dealt. You have learned all those 8 patterns: one pair, two pairs, three of a kind, straight, flush, full house, four of a kind, and straight flush (with royal flush a special kind of straight flush).

Note ace is counted as both 1 point and 14 points. So in counting straight, A2345 and 10JQKA are both valid.

Compute / derive the number of ways for these 8 patterns, show the formula and the numbers. Then rank these 8 patterns from highest rank royal flush with the number of ways to lowest rank one pair also with the number of ways. You may think of tabulating these as well to make it easy to read. Using C(52, 5), the number of hands (almost equal to 2.6 millions), also calculate and show the probabilities of each of these 8 ranks.

Eyeglassomatic manufactures eyeglasses for different retailers. The number of days it takes to fix defects in an eyeglass and the probability that it will take that number of days are in the table. Table #5.1.8: Number of Days to Fix DefectsNumber of daysProbabilities

1 24.9%

2 10.8%

3 9.1%

4 12.3%

5 13.3%

6 11.4%

7 7.0%

8 4.6%

9 1.9%

10 1.3%

11 1.0%

12 0.8%

13 0.6%

14 0.4%

15 0.2%

16 0.2%

17 0.1%

18 0.1%

State the random variable.

b.)Draw a histogram of the number of days to fix defects

c.)Find the mean number of days to fix defects.

d.)Find the variance for the number of days to fix defects

. e.)Find the standard deviation for the number of days to fix defects.

f.)Find probability that a lens will take at least 16 days to make a fix the defect.

g.)Is it unusual for a lens to take 16 days to fix a defect?

h.)If it does take 16 days for eyeglasses to be repaired, what would you think?

Suppose small aircraft arrive at a certain airport according to a Poisson process with rate α = 8 per hour, so that the number of arrivals during a time period of t hours is a Poisson rv with parameter

μ = 8t.

What is the probability that at least 7 small aircraft arrive during a 1-hour period?

What is the probability that at least 11 small aircraft arrive during a 1-hour period?

What is the probability that at least 23 small aircraft arrive during a 2.5-hour period?

What is the probability that at most 11 small aircraft arrive during a 2.5-hour period?

Q2. According to a Bon Appetit poll, 38% of people prefer chocolate ice cream. Use the binomial formula for calculating probabilities in a., b. and (ii).

(i) If 10 people are chosen at random, a. What is the probability that none prefer chocolate ice cream? b. What is the probability that only one prefers chocolate ice cream? c. What is the probability that more than one prefer chocolate ice cream? d. What is the expected number that prefer chocolate ice cream?

(ii) If 22 people are chosen at random, what is the probability that exactly 11 prefer chocolate ice cream?