Question

The distribution ages for students at Western University has a mean of m = 22 and a standard deviation of s = 4. Assume the distribution is normal.

a) What is the probability of selecting a random sample of n = 16 with an average age greater than 23?

b) What is the probability of selecting a random sample of n = 16 with an average age of less than 20?

c) What is the probability of selecting a random sample of n = 16 with an average age is between 19 and 23?

Answer 1

Solution :

Given that ,

= 22

= / n = 4 / 16 = 1

a) P( > 23) = 1 - P( < 23)

= 1 - P[( - ) / < (23 - 22) / 1 ]

= 1 - P(z < 1.00)   

= 1 - 0.8413

= 0.1587

b) P( < 20) = P(( - ) / < (20 - 22) / 1)

= P(z < -2.00)

Using z table

= 0.0228

c) P(19 < < 23)  

= P[(19 - 22) / 1 < ( - ) / < (23 - 22) / 1)]

= P(-3.00 < Z < 1.00)

= P(Z < 1.00) - P(Z < -3.00)

Using z table,  

= 0.8413 - 0.0013

= 0.8400