The random variable x has a normal distribution with standard deviation 25. It is known that the probability that x exceeds 150 is .90. Find

Question

The random variable x has a normal distribution with standard deviation 25. It is known that the probability that x exceeds 150 is .90. Find the mean

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Hailey 2 weeks 2022-01-07T08:33:18+00:00 2 Answers 0 views 0

Answers ( )

    0
    2022-01-07T08:35:04+00:00

    Answer: 182

    Step-by-step explanation:

    In the attachment

    0
    2022-01-07T08:35:14+00:00

    Answer:

     \mu= 150 +1.28*25 =182

    Step-by-step explanation:

    Previous concepts

    Normal distribution, is a “probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean”.

    The Z-score is “a numerical measurement used in statistics of a value’s relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean”.  

    Solution to the problem

    Let X the random variable that represent the variable of a population, and for this case we know the distribution for X is given by:

    X \sim N(\mu,25)  

    Where \mu and \sigma=25

    We know the following condition:

     P(X>150) = 0.9

    For this case we can use the z score formula given by:

    z=\frac{x-\mu}{\sigma}

    And we can find a z score that accumulates 0.9 of the area on the left and 0.1 on the right and this value is:  z= -1.28

    Becuase P(Z<-1.28) =0.1 and P(Z>-1.28) = 0.9

    So then if we use the z score formula we got:

     \frac{150-\mu}{25} = -1.28

    And if we solve for the mean we got:

     \mu= 150 +1.28*25 =182

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