Ask Question
16 May, 13:28

According to a report, 74.1 % of murders are committed with a firearm. (a) If 200 murders are randomly selected, how many would we expect to be committed with a firearm? (b) Would it be unusual to observe 167 murders by firearm in a random sample of 200 murders? Why? (a) We would expect nothing to be committed with a firearm. (b) Choose the correct answer below. A. No, because 167 is less than mu minus 2 sigma. B. Yes, because 167 is between mu minus 2 sigma and mu plus 2 sigma. C. Yes , because 167 is greater than mu plus 2 sigma. D. No , because 167 is between mu minus 2 sigma and mu plus 2 sigma. E. No, because 167 is greater than mu plus 2 sigma.

+4
Answers (1)
  1. 16 May, 16:21
    0
    (a) We would expect 148.2 murders to be committed with a firearm.

    (b) Yes , because 167 is greater than μ + 2σ.

    Step-by-step explanation:

    Let X = number of murders that are committed with a firearm.

    The probability that a murder is committed with a firearm is, p = 0.741.

    (a)

    A random sample of n = 200 murders are selected.

    A murder being committed with a firearm is independent o the others.

    The random variable X follows a Binomial distribution with parameters n = 200 and p = 0.741.

    The expected value of a Binomial random variable is:

    E (X) = n * p

    Compute the expected number of murder committed with a firearm in the sample of 200 murders as follows:

    E (X) = n * p

    = 200 * 0.741

    = 148.2

    Thus, the expected number of murder committed with a firearm is 148.2.

    (b)

    According to the rule of thumb, data values that are more than two standard deviations away from the mean are considered as unusual.

    That is, if X is unusual then:

    X <μ - 2σ or X> μ + 2σ

    The value that is considered unusual here is,

    X = 167.

    Check whether 167 murders with firearm are unusual or not as follows:

    μ ± 2σ = np ± (2 * √np (1 - p))

    = 148.2 ± 6.1955

    = (142.0045, 154.3955)

    ≈ (142, 154)

    The value 167 lies outside this range or X > μ + 2σ ⇒ 167 > 154.

    Thus, concluding that it would be unusual to observe 167 murders by firearm in a random sample of 200 murders.

    Correct option:

    Yes , because 167 is greater than μ + 2σ.
Know the Answer?
Not Sure About the Answer?
Find an answer to your question ✅ “According to a report, 74.1 % of murders are committed with a firearm. (a) If 200 murders are randomly selected, how many would we expect ...” in 📘 Mathematics if you're in doubt about the correctness of the answers or there's no answer, then try to use the smart search and find answers to the similar questions.
Search for Other Answers