Question

10. The population mean of annual salary for plumbers is $46,700, with a standard deviation of $5600. A random sample of 42 plumbers is drawn from this population. Find the probability that the mean salary of the sample is (a) less than $44,000. (b) between $40,000 and $51,000 (c) more than $55,000

Answer 1

a) let X: annual salary has mean = $46700 and standard deviation = $5600

We have to find P( xbar < 44000)

P( xbar < 44000) = P[ (xbar - )/(/√n) < (44000-46700)/(5600/√42)]

P( xbar < 44000) = P( Z < -3.12)

P(xbar < 44000) = 0.0009

b) P( 40000< xbar < 51000)

= P[ (40000-)/(/√n) < (xbar - )/(/√n) < (51000-)/(/√n) ]

= P ( -7.75 < Z < 4.98)

P( 40000 < xbar < 51000) = 1

c) P( xbar > 55000) = P[(xbar -)/(/√n) > (55000-46700)/(5600/√42)

P( xbar > 55000) = P( Z > 9.61)

P( xbar > 55000) = 0.0000