Question

You would like to study the weight of students at your university. Suppose the average for all university students is 159 with a SD of 27 lbs, and that you take a sample of 31 students from your university.

a) What is the probability that the sample has a mean of 160 or more lbs?
probability =

b) What is the probability that the sample has a mean between 164 and 167 lbs?
probability =

Answer 1

Solution :

Given that,

mean = = 159

standard deviation = = 27

n = 31

=  159

= / n = 27 31 = 4.8493

a ) P ( > 160 )

= 1 - P ( <160 )

= 1 - P (  - /) < ( 160 - 159 / 4.8493)

= 1 - P ( z < 1 / 4.8493 )

= 1 - P ( z <0.21)

Using z table

= 1 - 0.5832

= 0.4168

Probability =0.4168

b) P ( 164 < < 167 )

P ( 164- 159 / 4.8493) < (   - /  - / ) < ( 167- 159 / 4.8493)

P ( 5 / 4.8493 < z < 8 / 4.8493 )

P (1.03 < z < 1.65)

P ( z < 1.65 ) - P ( z < 1.03)

Using z table

=0.9505 - 0.8485

= 0.1020

Probability = 0.1020