Question

Suppose that at a large state university graduate research assistants are paid by the hour. Data from the personnel office show the distribution of hourly wages paid to graduates across the campus is approximately normal with a mean of $15.50 and a standard deviation of $4.00. Determine:

a. the probability of selecting at random from personnel files a graduate student who earns an hourly wage of $20 or more.

b. the probability of selecting at random from personnel files a graduate assistant who earns between $11 and $13 per hour

. c. the probability of selecting at random from the personnel files a graduate assistant whose hourly wage is extreme in either direction—either $10 or below or $21 and above.

Answer 1

Solution(a)
Mean = $15.50
Standard deviation = $4
Solution(a)
P(Xbar>=20) = 1-P(Xbar<20)
Z = (20-15.5)/4 = 1.125
From Z table we found p-value as follows:
P(Xbar>=20) = 0.1303
so there is 13.03% probability that who earns an hourly wage of $20 or more.
Solution(b)
P(11<Xbar<13) = P(Xbar<13)-P(Xbar<11)
Z = (11-15.50)/4 = -1.125
Z = (13-15.5)/4 = -0.625

P(11<Xbar<13) = 0.266-0.1303 = 0.1357

Solution(c)
P(Xbar<=10)
Z = (10-15.5)/4 = -1.375
P(Xbar>=21)
Z = (21-15.5)/4 = 1.375
P = 0.0838+0.0838 = 0.1676