Question

Apply the Central Limit Theorem for Sample Means A population of values has a normal distribution with μ = 220 and σ = 33.8. You intend to draw a random sample of size n = 35.

Find the probability that a single randomly selected value from the population is less than 224.

Answer 1

Given,

= 220

= 33.8

n = 35

Now calculate p(x < 224)

p(x < 224) = 0.5 + p(0 < z < x-/(/n))

= 0.5 + p(0 < z < 224-220/(33.8/35))

= 0.5 + p(0 < z < 0.70)

= 0.5 + 0.2580

p(x < 224) = 0.7580

Therefore probability that single randomly selected value from the population is less than 224 is 0.7580.