Suppose a population has a mean of 90 and a standard deviation of 28.If a random sample of size 49 is drawn from the population, the probability of drawing a sample with a mean between 85 and 95 is ___.
A)0.1056
B)0.3944
C)0.7888
D)0.2112
E)0.5000

Question

Quizplus · Accepted Answer

First, we need to convert the problem into standard normal distribution using the formula:

z = (x - μ) / (σ / sqrt(n))

where:
z = standard normal distribution (z-score)
x = sample mean
μ = population mean (given as 90)
σ = population standard deviation (given as 28)
n = sample size (given as 49)

Plugging in the values:

z1 = (85 - 90) / (28 / sqrt(49)) = -1.25
z2 = (95 - 90) / (28 / sqrt(49)) = 1.25

Next, we look up the probabilities associated with the z-scores using the standard normal distribution table or calculator. The probability of getting a z-score between -1.25 and 1.25 is:

P(-1.25 < z < 1.25) = P(z < 1.25) - P(z < -1.25)
= 0.8944 - 0.1056
= 0.7888

Therefore, the probability of drawing a sample with a mean between 85 and 95 is 0.7888 or approximately 0.79. The best choice is C.

Suppose a Population Has a Mean of 90 and a Standard