Question

Leave answers as decimals (not percents). When necessary, round final answers to 4 decimal places. Write out Excel Formula used to calculate answer

The manufacturer of a certain electronic component claims that they are designed to last 4 years because they believe that customers will typically replace their device before then. A journalist who specializes in technology is skeptical, and he conducts a study where he measures how long these components truly last. He found that 7% of the components failed after 3 years, 13% failed after 4 years, and 72% failed after 5 years. Suppose a group of 30 randomly selected components are tested after 4 years. Let X be the number of these components that fail after 4 years.

a. Choose one: X is a binomial random variable X is a normal random variable

b. Find P(x < 3)

c. Find the probability that, of these 30 components, between 5 and 8 of them will fail after 4 years.

Answer 1

a)

X is a binomial random variable

b)

P(x < 3) =1-0.07-0.13-0.72=0.08

c)

here for binomial distribution ; parameter n=30 and p=0.13

P(5<=X<=8)=0.3383

( please try 0.1532 if 5 and 8 are exclusive)