Question

Central limit theorem: Sample mean The mean salary offered to students who are graduating from Coastal State University this year is $24.260, with a standard deviation of $3712. A random sample of 75 Coastal State students graduating this year has been selected. What is the probability that the mean salary offer for these 75 students is $25,000 or more? Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places. ?

Answer 1

Solution :

Given that ,

mean = $\mu$ = 24260

standard deviation = $\sigma$ = 3712

n = 75

$\mu$
_T
= $\mu$ = 24260 and

$\sigma$
_T
= $\sigma$ / $\sqrt$ n = 3712 / $\sqrt$ 75 = 428.6248

P(
T
$\geq$ 25000) = 1 - P(
T
< 25000)

= 1 - P((
T
- $\mu$
_T
) / $\sigma$
_T
< (25000 - 24260) / 428.6248)

= 1 - P(z < 1.73)

= 1 - 0.9582 Using standard normal table.

= 0.0418

Probability = 0.0418