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In Hawaii, January is a favorite month for surfing since 60% of the days have a...

In Hawaii, January is a favorite month for surfing since 60% of the days have a surf of at least 6 feet.† You work day shifts in a Honolulu hospital emergency room. At the beginning of each month you select your days off, and you pick 7 days at random in January to go surfing. Let r be the number of days the surf is at least 6 feet.

(a) Make a histogram of the probability distribution of r.

(b) What is the probability of getting 4 or more days when the surf is at least 6 feet? (Round your answer to three decimal places.)

(c) What is the probability of getting fewer than 2 days when the surf is at least 6 feet? (Round your answer to three decimal places.)

(d) What is the expected number of days when the surf will be at least 6 feet? (Round your answer to two decimal places.)
days

(e) What is the standard deviation of the r-probability distribution? (Round your answer to three decimal places.)
days

(f) Can you be fairly confident that the surf will be at least 6 feet high on one of your days off? Explain. (Round your answer to three decimal places.)

---Select--- Yes No , because the probability of at least 1 day with surf of at least 6 feet is and the expected number of days when the surf will be at least 6 feet is ---Select--- less than equal to greater than one.

Expert Solution

In Hawaii, January is a favorite month for surfing since 60% of the days have a surf of at least 6 feet. This is same as

the probability that any given day in January has a surf of at least 6 feet is 0.60

you pick 7 days at random in January to go surfing. Let R be the number of days the surf is at least 6 feet. We can say that R has a Binomial distribution with parameters, number of trials (number of days gone on surfing) n=7 and success probability (the probability that any given day in January has a surf of at least 6 feet) p=0.60

The probability that R=r days when the surf is at least 6 feet is

We can get the value of P(R=r) for r=0,1,...,7 as below

We can get the following table of probabilities

r	P(R=r)
0	0.0016
1	0.0172
2	0.0774
3	0.1935
4	0.2903
5	0.2613
6	0.1306
7	0.0280

(a) Make a histogram of the probability distribution of r.

We create a bar chart using the table

(b) What is the probability of getting 4 or more days when the surf is at least 6 feet? (Round your answer to three decimal places.)

ans: the probability of getting 4 or more days when the surf is at least 6 feet is 0.710

(c) What is the probability of getting fewer than 2 days when the surf is at least 6 feet? (Round your answer to three decimal places.)

ans: the probability of getting fewer than 2 days when the surf is at least 6 feet is 0.019

(d) What is the expected number of days when the surf will be at least 6 feet? (Round your answer to two decimal places.)
days

The expected value of R using the formula for Binomial expectation is

ans: the expected number of days when the surf will be at least 6 feet is 4.20 days

(e) What is the standard deviation of the r-probability distribution? (Round your answer to three decimal places.)
days
The standard deviation of R using the formula for Binomial distribution

ans: the standard deviation of the r-probability distribution is 1.296 days

(f) Can you be fairly confident that the surf will be at least 6 feet high on one of your days off? Explain. (Round your answer to three decimal places.)

the probability of at least 1 day with surf of at least 6 feet is

ans: Yes , because the probability of at least 1 day with surf of at least 6 feet is 0.998 and the expected number of days when the surf will be at least 6 feet is greater than one.

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