The owners of a motel in Florida have noticed that in the long run, about 40% of the people who stop and inquire about a room for the night actually rent a room. (a) How many inquires must the owner answer to be 99% sure of renting at least one room? inquiries (b) If 20 separate inquiries are made about rooms, what is the expected number of inquiries that will result in room rentals? inquiries

(a) n = 9 inquiries

The owner must answer 9 inquiries to be 99% sure of renting at least one room.

(b) E(x) = 8 inquiries

Therefore, the expected number of inquiries that will result in room rentals is 8.

Step-by-step explanation:

The given problem can be solved by Binomial distribution.

Let x be the people who stop and inquire about a room for the night actually rent a room.

P(x) = ⁿCₓ pˣ (1 - p)ⁿ⁻ˣ  

Where n is the number of trials, x is the variable of interest and p is the probability of success.  

(a) How many inquires must the owner answer to be 99% sure of renting at least one room?

For the given case, we have p = 0.40 and we want to find n such that

P(x ≥ 1) = 0.99

we know that

P(x ≥ 1) = 1 - P(x < 1)

P(x ≥ 1) = 1 - P(x = 0)

So,

1 - P(x = 0) = 0.99

P(x = 0) = 1 - 0.99

P(x = 0) = 0.01

For x = 0 and p = 0.40

P(x = 0) =(ⁿC₀) (0.40)⁰ (1 - 0.40)ⁿ⁻⁰

0.01 = (1)(1)(0.60)ⁿ

0.01 = 0.60ⁿ

ln(0.01) = ln(0.60ⁿ)

ln(0.01) = n ln(0.60)

n = ln(0.01)/ln(0.60)

n = 9.01

Rounding off to nearest whole number

n = 9 inquiries

Therefore, the owner must answer 9 inquiries to be 99% sure of renting at least one room.

(b) If 20 separate inquiries are made about rooms, what is the expected number of inquiries that will result in room rentals?

The expected number of inquiries is given by

E(x) = n×p

For the given case, we have n = 20 and p = 0.40

E(x) = 20×0.40

E(x) = 8 inquiries

Therefore, the expected number of inquiries that will result in room rentals is 8.

d

gimmee one of those gold crowns!

~coco

answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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