Answer to Question #260241 in Statistics and Probability for Ynamurata

Question

2. A study shows that length of the careers of professional basketball players are nearly normally distributed, with a mean of 6.1 years and a standard deviation of 1.8 years.

Answer 1

Question is incomplete. We can add last line as ''What percent of professional basketball players have a career of more than 9 years?

Solution:

$\text{Given: Mean }(\mu) = 6.1\ \text{ year} \\\text{Standard deviation}\ (\sigma)=1.8 \\\begin{aligned} \\P(x>9) &=1-P(x<9) \\ \\&=1-p\left(\frac{x- \mu}{\sigma}<\frac{9-6.1}{1.8}\right) \\ \\&=1-P\left(z<\frac{2.9}{1.8}\right) \\ \\&=1-P(z<1.61) \\ \\&=1-0.9463 \\ \\&=0.0537 \\ \\&=5.37 \% \end{aligned}$

$\\\therefore 5.37 \%$ is the percent of professional basketball player have a career of more than 9 years.