# 1. Continuous probability distribution. Right triangle, base going from 0 to 5 on the x axis

Question

1. Continuous probability distribution. Right triangle, base going from 0 to 5 on the x axis. The high point of the right triangle exist at the point where x equals five. Find the area (the probability) between 3 and 5. Also, just for fun, obtain the mean using calculus.

2. Page 254, problem 32

3. Page 254, problem 34

4. If a variable follows the binomial distribution, and , what is the probability of exactly 10 successes, if p is equal to .6?

a) use the binomial

b) Use the normal to approximate the binomial

5. Using the same information given in number 4,

a) What is the probability of 15 or more successes?, using the normal to approximate

b) What is the probability of greater than 8 successes?

c) What is the probability of equal to or less than 11 failures?

6. A Myrtle Beach resort hotel has 120 rooms. In the spring months, hotel room occupancy is approximately 75%.

a) what is the probability that at least half of the rooms are occupied on a given day?

b) what is the probability that 100 or more rooms are occupied on a given day?

c) what is the probability that 80 or fewer rooms are occupied on a given day?

7. Using algebra, go from equation A to equation B

A. P[µ – z( ) < < µ + z( ) ] = 1 – ?

B. P[ -z( ) < µ < + z( ) ] = 1 – ?

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