Question

The distribution ages for students at Columbia 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,

mean = = 22

standard deviation = = 4

n = 16

= 22

= / n = 4 16 = 1

a ) P ( > 23)

= 1 - P ( < 23 )

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

= 1 - P ( z < 1 / 1 )

= 1 - P ( z < 1 )

Using z table

= 1 -0.8413

= 0.1587

Probability = 0.1587

b ) P( < 20 )

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

P ( z < - 2 / 1 )

P ( z < - 2 )

= 0.0228

Probability = 0.0228

c ) P (19 < < 23 )

P ( 19 - 22 / 1 ) < ( - / ) < ( 23 - 22 / 1)

P ( - 3 / 1 < z < 1 / 1 )

P (-1 < z < 1 )

P ( z < 1 ) - P ( z < -3)

Using z table

= 0.8413 - 0.0013

= 0.8400

Probability = 0.8400