# Statistics - Normal Distribution and Binomials

1. Suppose 1.5 percent of the sim cards on new Motorola cell phones are defective. For a random sample of 10 sim cards, use the binomial distribution to find the probability that:

a. None of the antennas is defective.

b. Three or more of the antennas are defective.

c. At most 3 are defective.

d. All 10 antennas are defective.

2. The amounts of money requested on loan applications at United Savings follow the normal distribution, with a mean of $270,000 and a standard deviation of $35,000. A loan application is received this morning. What is the probability:

a. The amount requested is $270,000 or more?

b. The amount requested is $300,000 or more?

c. The amount requested is between $265,000 and $365,000?

d. The amount requested is $365,000 or more?

https://brainmass.com/statistics/normal-distribution/199330

#### Solution Preview

(1) p = 1.5% = 0.015, q = 1 - p = 0.985, n = 10

The binomial probability formula is P(r successes, n trials) = nCr p^r q^(n - r)

(a) P(0) = 10C0 0.015^0 0.985^10 = 0.85973

(b) P(3 or more) = 1 - [P(0) + P(1) + P(2)]

= 1 - 10C0 0.015^0 ...

#### Solution Summary

Neat and step-by-step solutions are provided.