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The heights of all female college basketball players produce a distribution that is approximately normal with a mean of 67.82 and a standard deviation of 2.06.The probability that the height of a randomly selected female college basketball player is less than 67.2 inches, rounded to three decimal places, is:

Answer :

SOLUTION

To solve this we will find the Z score for the distribution, we will use

[tex]\begin{gathered} Z=\frac{x-\mu}{\sigma} \\ where\text{ Z = standard score } \\ x=\text{ observed value = 67.2} \\ \mu=\text{ mean of the sample = 67.82} \\ \sigma=\text{ standard deviation = 2.06} \end{gathered}[/tex]

Putting the values into the equation we have

[tex]\begin{gathered} Z=\frac{67.2-67.82}{2.06} \\ Z=\frac{-0.62}{2.06} \\ Z=-0.30097 \end{gathered}[/tex]

Using the Zscore calculator, we have

[tex]P\left(xHence the answer is 0.382 to three decimal places

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