A scientist studying water quality measures the lead level in parts per billion (ppb) at each of 49 randomly chosen locations along a water

Question

A scientist studying water quality measures the lead level in parts per billion (ppb) at each of 49 randomly chosen locations along a water line. Suppose that the lead levels across all the locations on this line are strongly skewed to the right with a mean of ppb17 and a standard deviation of 14ppb. Assume that the measurements in the sample are independent.

Required:
What is the probability that the mean lead level from the sample of 49 measurements T is less than 15 ppb?

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Khoii Minh 5 years 2021-07-19T21:53:42+00:00 2 Answers 35 views 0

Answers ( )

  1. diemthu
    0
    2021-07-19T21:55:30+00:00
    Reply

    Answer:

    The probability that the mean lead level from the sample of 49 measurements T is less than 15 ppb

    P(x⁻< 15) = 0.1587

    Step-by-step explanation:

    Step(i):-

    Given that the size of the sample ‘n’ =49

    Mean of the Population = 17ppb

    The standard deviation of the population = 14ppb

    Let ‘X’ be the random variable in a normal distribution

    Z = \frac{x-mean}{\frac{S.D}{\sqrt{n} } } = \frac{15-17}{\frac{14}{\sqrt{49} } } = -1

    Step(ii):–

    The probability that the mean lead level from the sample of 49 measurements T is less than 15 ppb

    P(x⁻< 15) = P(Z<-1) = 1-P(Z>-1)

                                 = 1-(0.5+A(-1))

                                 = 0.5 – A(1)

                                = 0.5-0.3413

                                = 0.1587

    Final answer:-

    The probability that the mean lead level from the sample of 49 measurements T is less than 15 ppb

    P(x⁻< 15) = 0.1587

  2. Cherry
    0
    2021-07-19T21:55:37+00:00
    Reply

    Answer:

    0.16

    Step-by-step explanation:

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