Question

A normal population has mean = 7 and standard deviation - 7. (a) What proportion of the population is less than 19? (b) What is the probability that a randomly chosen value will be greater than 47 Round the answers to four decimal places Part 1 of 2 The proportion of the population less than 19 is Part 2 of 2 The probability that a randomly chosen value will be greater than 4 is

Answer 1

If X follows Normal distribution then

(x - $\mu$ ​​​​​​) /$\sigma$ follows standard normal distribution

A.

P(X < 19)

= P{(x -$\mu$​​​​​​) $\sigma$ < (19 - 7)/7}

= P( Z < 1.71)

= 1 - P( Z > 1.71)

= 1 - 0.0436

= 0.9564

0.9564 proportion of population is less than 19

B.

P( X > 4)

= P{(x -$\mu$​​​​​​) $\sigma$ > (4 - 7)/7}

= P( Z > - 0.43)

= 1 - P(Z < - 0.43)

= 1 - P( Z > 0.43)

(since standard normal distribution is symmetric around zero)

= 1 - 0.3336

= 0.6664