A local concert center reports that it has been experiencing a 15% rate of no-shows on advanced reservations. Among 150 advanced reservations, find the probability that there will be fewer than 20 no-shows

Given Information:  

Number of advanced reservations = n = 150  

Probability of success = p = 15% = 0.15

Required Information:  

Probability that there will be fewer than 20 no-shows = ?

P(X < 19.5) = 24.83 %  

Explanation:  

The mean is given by

μ = np

Where n is the number of advanced reservations and p is the probability of no shows

μ = 150*0.15

μ = 22.5

since np ≥ 5 and n(1-p) = 127.5 ≥ 5 we can proceed with normal approximation to binomial distribution

The standard deviation is given by

σ = √npq

Where q is given by

q = 1 - p

q = 1 - 0.15

q = 0.85

σ = √(150*0.15*0.85)

σ = 4.37

We want to find out the probability of fewer than 20 no shows among the 150 advanced reservations given the success rate of no shows is 15% and correction factor of 0.5

X = 20 - 0.5 = 19.5

P(X < 19.5) = P(z < (x - μ)/σ)

P(X < 19.5) = P(Z < (19.5 - 22.5)/4.37)

P(X < 19.5) = P(Z < -0.68)

The z-score corresponding to -0.68 is found from the z-table that is 0.2483

P(X < 19.5) = 0.2483

P(X < 19.5) = 24.83%  

Therefore, there is 24.83%  probability that there will be fewer than 20 no-shows among the 150 advanced reservations having a 15% rate of no-shows.

henry ordered 5 large pizzas

step-by-step explanation:

sorry no step by step

answer: there are x+184 pages in olivia's book.

step-by-step explanation:

let the total number of pages in the book which olive has already read be x.

then if olive has 184 pages left to read, then the total number of pages are in olive's book= pages she has read+pages she has left to read

therefore, the total number of pages in olivia's book=

hence, there are x+184 pages in olivia's book.