Question

2.

7% of the customers of a mortgage company default on their payments.

A sample of six customers is selected.

What is the probability that exactly two customers in the sample will default on their payments?

(NOTE: Round your FINAL answer to the nearest 4 decimal points. For example, 0.0223 or 0.2579)

5.

An airline has determined that 12% of its international flights are not on time. Use the normal approximation to the binomial distribution to answer the following questions.

What is the probability that of the next 50 international flights, three or less will not be on time?

(Note: Note that your FINAL answer is rounded to 2 digits - so it will look something like 0.26 or 0.39 or 0.07)

Answer 1

2)

X ~ binomial (n,p)

Where n = 6 , p = 0.07

P(X) = ⁿC_x p^x ( 1 -p)^n-x

So

P (X = 2) = ⁶C₂ 0.07² 0.93⁴  

= 0.0550

5)

Mean = np = 50 * 0.12 = 6

Standard deviation = Sqrt ( n p( 1 - p) )

= sqrt( 50 * 0.12 * 0.88)

= 2.297825

Using normal approximation

P (X < x) = P( Z <= x+0.5 - mean / SD)

So,

P( X <= 3) = P( Z < 3.5 - 6 / 2.297825)

= P( Z < -1.0880)

= 0.14 (From Z table)