Question

normal population has a mean of 65 and a standard deviation of 13. You select a random sample of 16.

Compute the probability that the sample mean is: (Round your z values to 2 decimal places and final answers to 4 decimal places):

1. Greater than 67.

2. Less than 64.

3. Between 64 and 67.

Answer 1

Solution :

Given that,

mean = = 65

standard deviation = = 13

n = 16

= 65

= / n = 13 16 = 3.25

a ) P ( > 67 )

= 1 - P ( < 67 )

= 1 - P ( - / ) < ( 67 - 65 / 3.25)

= 1 - P ( z < 2 / 3.25 )

= 1 - P ( z < 0.61)

Using z table

= 1 - 0.7291

= 0.2709

Probability = 0.2709

b ) P( < 64 )

P ( - / ) < ( 64 - 65 / 3.25)

P ( z < -1 / 3.25 )

P ( z <0.963)

= 0.8322

Probability = 0.8322

c ) P (64 < < 67 )

P ( 64 - 65 / 3.25) < ( - / ) < ( 67 - 65 / 3.25)

P ( - 1 / 3.25 < z < 2 / 3.25 )

P (-0.31 < z < 0.61)

P ( z < 0.61 ) - P ( z < -0.31)

Using z table

= 0.7291 - 0.3783

= 0.3508

Probability = 0.3508