If the pH level of the reservoir is ok, the results at each location will have varying results, with an average pH of 8.5 and a standard dev

Question

If the pH level of the reservoir is ok, the results at each location will have varying results, with an average pH of 8.5 and a standard deviation of 0.22. If the pH level of the reservoir is ok, what is the probability that the sample average is LESS than 8.47

in progress 0
Mary 2 months 2021-10-17T14:59:11+00:00 1 Answer 0 views 0

Answers ( )

    0
    2021-10-17T15:00:47+00:00

    Answer:

    44.43% probability that the sample average is LESS than 8.47

    Step-by-step explanation:

    Problems of normally distributed samples are solved using the z-score formula.

    In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

    Z = \frac{X - \mu}{\sigma}

    The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

    In this problem, we have that:

    \mu = 8.5, \sigma = 0.22

    If the pH level of the reservoir is ok, what is the probability that the sample average is LESS than 8.47

    This is the pvalue of Z when X = 8.47. So

    Z = \frac{X - \mu}{\sigma}

    Z = \frac{8.47 - 8.5}{0.22}

    Z = -0.14

    Z = -0.14 has a pvalue of 0.4443.

    44.43% probability that the sample average is LESS than 8.47

Leave an answer

45:7+7-4:2-5:5*4+35:2 =? ( )