Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.)

μ = 8; σ = 2 P(7≤x≤111)=

Answer:

Given Data :

The population mean $(\mu )=8$

The population standard deviation $(\sigma )=2$

→ The Indicated Probability for P(Seven Less Than or Equal to X Less Than or Equal to One Hundred Eleven) :

$$P(7<x<11)=P(\frac{7–8}{2}<\frac{x–\mu }{\sigma }<\frac{11–8}{2})$$ $$=P(-0.5<z<1.5)$$ $$=P(z<1.5)–P(z<-0.5)$$ $$=0.9332–0.3085$$ $$=0.6247$$