Question

A random variable having a normal distribution with ? = 20 ??? ?? = 9 find the probabilities that it will:

a. Take on a value less than 17

b. Between 13 and 26

Answer 1

Solution :

a.

P(x < 17) = P[(x - ) / < (17 - 20) / 9]

= P(z < -0.3333)

= 0.3695

Probability = 0.3695

b.

P(13 < x < 26) = P[(13 - 20)/ 9) < (x - ) /  < (26 - 20) / 9) ]

= P(-0.7778 < z < 0.6667)

= P(z < 0.6667) - P(z < -0.7778)

= 0.7475 - 0.2183

= 0.5292

Probability = 0.5292