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    Statistics - Normal Distribution and Binomials

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    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?

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    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 ...

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