Question

Assume the random variable x is normally distributed with mean mu equals80 and standard deviation sigma equals 5. Find the indicated probability. ​P(68less thanxless than71​) ​P(68less thanxless than71​)equals nothing ​(Round to four decimal places as​ needed.)

Answer 1

Given ,

$\mu$ = 80 , $\sigma$ = 5

We convert this to standard normal as

P(X < x) = P(Z < (x - $\mu$ ) / $\sigma$ )

So,

P(68 < X < 71) = P(X < 71) - P(X < 68)

= P(Z < (71 -80) / 5 ) - P(Z < (68 -80) / 5 )

= P(Z < -1.8) - P(Z < -2.4)

= 0.0359 - 0.0082

= 0.0277