Question

A random sample of size 16 was taken from a normally distributed population with a population mean 26 and a population standard deviation 5.

Determine each of the following.

a) What range best describes P(X<24.10) ?

1. Less than 0.5

2. Greater than 0.5

3. Cannot be determined

b) What is P(Xˉ<24.1) ? Enter your response to at least 3 decimal places.

Answer 1

Solution :

Given that,

mean = = 26

standard deviation = = 5

a ) P( x < 24.10)

P ( x - / ) < ( 26 - 24.10 / 5)

P ( z < 1.90 / 5 )

P ( z < 0.38)

= 0.6480

Probability = 0.6480

Option 2 ) is correct.

Greater than 0.5

b ) n = 16

= 26

₌ / n = 5 16 = 1.25

P( < 24.10)

P ( - / ) < ( 26 - 24.10 /1.25)

P ( z < 1.90 / 1.25 )

P ( z < 1.52 )

= 0.9357

Probability = 0.936