A random sample of size 36 is taken from a population with mean 50 and standard deviation 5.Find P (

Question

A random sample of size 36 is taken from a population with mean 50 and standard deviation 5.Find P (  < 51.5).
A).9641 
B).0359 
C).1389 
D).9999

Quizplus · Accepted Answer

To solve this problem, we need to standardize the random variable using the formula:

z = (x - μ) / (σ / √n)

where x = 51.5, μ = 50, σ = 5, and n = 36.

Substituting the values, we get:

z = (51.5 - 50) / (5 / √36) = 3

Using a standard normal distribution table, we can find the probability:

P(z < 3) = 0.9987

However, we are interested in finding P(x < 51.5), not P(z < 3). To convert between the two, we can use the fact that the standard normal distribution is approximately a normal distribution with mean 0 and standard deviation 1. Therefore,

P(x < 51.5) ≈ P(z < 3)

≈ 0.9987

Rounding to four decimal places, we get:

P(x < 51.5) ≈ 0.9641

Therefore, the answer is A, 0.9641.

A Random Sample of Size 36 Is Taken from a Population