Weights were recorded for all nurses at a particular hospital, the mean weight for an individual nurse was 135 lbs. with a standard deviatio

Question

Weights were recorded for all nurses at a particular hospital, the mean weight for an individual nurse was 135 lbs. with a standard deviation of 15. If 19 nurses are selected at random, find the probability that the mean weight is between 125 and 130 lbs

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    2021-09-19T07:42:13+00:00

    Given:
    population mean, μ =135
    population standard deviation, σ = 15
    sample size, n = 19

    Assume a large population, say > 100,
    we can reasonably assume a normal distribution, and a relatively small sample.
    The use of the generally simpler formula is justified.

    Estimate of sample mean
    \bar{x}=\mu=135

    Estimate of sample standard deviation
    \s=\sqrt{\frac{\sigma^2}{n}}
    =\sqrt{\frac{15^2}{19}}=3.44124  to 5 decimal places.

    Thus, using the normal probability table,
    P(125<X<130)
    =P(\frac{125-135}{3.44124}<Z<\frac{130-135}{3.44124})
    =P(-2.90593<Z<-1.45297)
    =P(Z<-2.90593)=0.0018308
    =P(Z<-1.45297)=0.0731166

    Therefore 
    The probability that the mean weight is between 125 and 130 lbs 
    P(125<X<130)=0.0731166-0.0018308
    =0.0712858

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