1. Suppose 1.5 percent of the sim cards on new Motorola cell phones are defective. For a random sampleof 10 sim cards, use the binomialdistribution to find the probabilitythat:
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 meanof $270,000 and a standard deviationof $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?
(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 …
Neat and step-by-step solutions are provided.