# A normal population has a mean of 80.0 and a standard deviation of 14.0. Compute

Tahmid Knox 2021-10-17 Answered
A normal population has a mean of 80.0 and a standard deviation of 14.0. Compute the probability of a value 75.0 or less.

## Want to know more about Probability?

• Live experts 24/7
• Questions are typically answered in as fast as 30 minutes
• Personalized clear answers

### Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

gotovub

Mean of the normal distribution is \mu = 80 and the standard deviation is $$\displaystyle\sigma={14}$$
Let X be the random variable.
$$\displaystyle{P}{\left({X}{<}{75}\right)}={P}{\left({X}-\mu{<}{75}-\mu\right)}$$
$$\displaystyle={P}{\left({\frac{{{X}-\mu}}{{\sigma}}}{<}{\frac{{{75}-\mu}}{{\sigma}}}\right)}$$
$$\displaystyle={P}{\left({z}{<}{\frac{{{75}-{80}}}{{{14}}}}\right)}$$
$$\displaystyle={P}{\left({z}{<}{\frac{{-{5}}}{{{14}}}}\right)}$$
=P(z<-0.357)
=P(z>0.357)
=0.5-P(0 =0.5-0.14-6 (from Appendix B1.)
=0.3594