When circuit boards used in the manufacture of compact disc players are tested, the long-run percentage of defectives is 5%. Let X = the number of defective boards in a random sample of size n = 25, so X ~ Bin(25, 0.05). (Round your probabilities to three decimal places.)
(a) Determine P(X <_ 2).(b) Determine P(X >_ 5).(c) Determine P(1 <_ X <_ 4).(d) What is the probability that none of the 25 boards is defective?

(a) The value of P (X ≤ 2) is 0.873.

(b) The value of P (X ≥ 5) is 0.007.

(c) The value of P (1 ≤ X ≤ 4) is 0.716.

(d) The probability that none of the 25 boards is defective is 0.277.

Step-by-step explanation:

The random variable X is defined as the number of defective circuit boards.

It is provided that X follows a Binomial distribution with parameter n = 25 and p = 0.05.

The probability mass function of Binomial distribution is:

(a)

Compute the value of P (X ≤ 2) as follows:

P (X ≤ 2) = P (X = 0) + P (X = 1) + P (X = 2)

Thus, the value of P (X ≤ 2) is 0.873.

(b)

Compute the value of P (X ≥ 5) as follows:

P (X ≥ 5) = 1 - P (X < 5)

              = 1 - P (X = 0) - P (X = 1) - P (X = 2) - P (X = 3)+- P (X = 4)

Thus, the value of P (X ≥ 5) is 0.007.

(c)

Compute the value of P (1 ≤ X ≤ 4) as follows:

P (1 ≤ X ≤ 4) = P (X = 1) + P (X = 2) + P (X = 3) + P (X = 4)

Thus, the value of P (1 ≤ X ≤ 4) is 0.716.

(d)

Compute the probability of X = 0 as follows:

Thus, the probability that none of the 25 boards is defective is 0.277.

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.