The mean undergraduate cost for tuition, fees, room, and board for four-year institutions was $26,489 for a recent academic year. Suppose that the standard deviation is $3204 and that 36 four-year institutions are randomly selected. Find the probability that the sample mean cost for these 36 schools is Less than $25,000

0.00265

Step-by-step explanation:

We solve using the z score formula

z = (x-μ)/σ/√n

where

x is the raw score = $25,000

μ is the population mean = $26,489

σ is the population standard deviation = $3204

n = random number of samples = 36

For x < 25,000

z = 25000 - 26489/3204/√36

z = 25000 - 26489/3204/6

z = -1489/534

z = -2.78839

Probability value from Z-Table:

P(x<25000) = 0.0026485

Approximately = 0.00265

The probability that the sample mean cost for these 36 schools is Less than $25,000 is 0.00265