Question

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 1

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

`\begin{gathered} Z=(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}`

Putting the values into the equation we have

`\begin{gathered} Z=(67.2-67.82)/(2.06) \\ Z=(-0.62)/(2.06) \\ Z=-0.30097 \end{gathered}`

Using the Zscore calculator, we have

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