Question

According to the government of Ontario, the mean hourly wage of Ontarians is $20.58 with a standard deviation of $2.31. A random sample of 47 Ontarians is taken. What is the probability that the sample mean is greater than $21.30?

a) 0.3783

b) 0.0162

c) 0.6217

d) 0.9838

Answer 1

Solution :

Given that,

mean = = 20.58

standard deviation = =21.30

n = 47

= 20.58

  =  ( /n) = (2.31 / 47  ) = 0.3369

P ( > 21.30)

= 1 - P < 12.4 )

= 1 - P ( -  / ) < ( 21.30 - 20.58 / 0.3369)

= 1 - P ( z < 0.72 /0.3369 )

= 1 - P ( z < 2.4)

Using z table

= 1 -0.9838

= 0.0162

Probability = 0.0162

Option b ) is correct.