Question

A certain car brand is equipped with an engine in one of four sizes (in liters): 2.8, 3.0, 3.3, or 3.8. 10% of customers order the 2.8-liter engine, 40% from 3.0, 30% from 3.3 and 20% from 3.8. A random sample of 20 orders is selected for an audit. (3p)
a) What is the probability that the number of orders for the 2.8, 3.0, 3.3 and 3.8 liter engines are 3, 7, 6 and 4, respectively?

b) What is the probability that there are more than ten orders of 3.0-liter engines?

A. a) 0.00890 b) 0.1275
B. a) 0.00997 b) 0.2289
C. a) 0.00987 b) 0.2478
D. a) 0.00789 b) 0.879
E. a) 0.00995 b) 0.589

Answer 1

a) Here we need to use multinominal distribution to find the probability.

The required probability is as

b) Let X = number of order of  3.0-liter engines

So X follows binomial distribution with n = 20 and p = 0.40

Here we want to find P( X > 10) = 1 - P( X <= 10 )

Let's use excel

P( X <= 10 ) = "=BINOMDIST(10,20,0.4,1)" = 0.8725

P( X > 10) = 1 - P( X <= 10 ) = 1 - 0.8725 = 0.1275

So correct choice is A. a) 0.00890 b) 0.1275