Question

According to the government of Manitoba, the average hourly wages in the manufacturing sector are as follows: Alberta: $22.02, Ontario: $20.18, British Columbia: $20.05. Assume that in all three provinces, the standard deviation of hourly wages is $3. Suppose 40 workers are selected randomly from across Alberta and asked what their hourly wage is. What is the probability that the sample average will be between $21 and $22? Suppose 35 manufacturing workers are selected randomly from across Ontario. What is the probability that the sample average will exceed $23? Suppose 50 manufacturing workers are selected randomly from across British Columbia. What is the probability that the sample average will be less than $18.90?

Answer 1

Here population standard deviation is known so we will use z distribution to find the required probability

For Alberta, mean is 22.02

We need to find

As population is normal we can convert sample mean to z

Now for Ontario mean is 20.18

We need to find

As distribution is normal we can convert sample mean to z

For British Columbia mean is 20.05

We need to find

As distribution is normal we can convert sample mean to z