Major league baseball salaries averaged $3.26 million with a standard deviation of $1.2 million in a the past year. Suppose a sample of 100

Question

Major league baseball salaries averaged $3.26 million with a standard deviation of $1.2 million in a the past year. Suppose a sample of 100 major league players was taken this year. What is the approximate probability that the mean salary of the 100 players was less than $3.0 million?

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Ayla 2 days 2021-10-12T12:11:07+00:00 1 Answer 0

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    2021-10-12T12:12:57+00:00

    Answer:

    0.015 is the approximate probability that the mean salary of the 100 players was less than $3.0 million

    Step-by-step explanation:

    We are given the following information in the question:

    Mean, μ =$3.26 million

    Standard Deviation, σ = $1.2 million 100

    We assume that the distribution of salaries is a bell shaped distribution that is a normal distribution.

    Formula:

    z_{score} = \displaystyle\frac{x-\mu}{\sigma}

    Standard error due to sampling =

    \displaystyle\frac{\sigma}{\sqrt{n}} = \frac{1.2}{\sqrt{100}} = 0.12

    P(mean salary of the 100 players was less than $3.0 million)

    P(x < 3) = P(z < \displaystyle\frac{3-3.26}{0.12}) = P(z < -2.167)

    Calculating the value from the standard normal table we have,

    P(Z < -2.167) = 0.015 \\P( x < 3) = 1.5\%

    0.015 is the approximate probability that the mean salary of the 100 players was less than $3.0 million

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