The probability is 51​% that the sample mean will be between what two​ values, symmetrically distributed around the population​ mean? The lo

Question

The probability is 51​% that the sample mean will be between what two​ values, symmetrically distributed around the population​ mean? The lower bound is nothing inches. ​(Round to two decimal places as​ needed.) The upper bound is nothing inches. ​(Round to two decimal places as​ needed.)

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Luna 3 weeks 2021-12-29T04:02:39+00:00 1 Answer 0 views 0

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    2021-12-29T04:04:32+00:00

    Answer:

    The lower bound is, -z=-0.69 and the upper bound is z=0.69.

    Step-by-step explanation:

    Let the random variable X follows a normal distribution with mean μ and standard deviation σ.

    The the random variable Z, defined as Z=\frac{X-\mu}{\sigma} is standardized random variable also known as a standard normal random variable. The random variable  Z\sim N(0, 1).

    The standard normal random variable has a symmetric distribution.

    It is provided that P(-z\leq Z\leq z)=0.51.

    Determine the upper and lower bound as follows:

    P(-z\leq Z\leq z)=0.51\\P(Z\leq z)-P(Z\leq -z)=0.51\\P(Z\leq z)-[1-P(Z\leq z)]=0.51\\2P(Z\leq z)-1=0.51\\2P(Z\leq z)=1.51\\P(Z\leq z)=0.755

    Use a standard normal table to determine the value of z.

    The value of z such that P (Z ≤ z) = 0.755 is 0.69.

    The lower bound is, -z=-0.69 and the upper bound is z=0.69.

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