A random sample of size 36 is taken from a population with mean 50 and standard deviation 5.Find P ( 50.5).
A).0002
B).7257
C).2743
D).1389

Question

A random sample of size 36 is taken from a population with mean 50 and standard deviation 5.Find P (  > 50.5).
A).0002 
B).7257 
C).2743 
D).1389

Quizplus · Accepted Answer

We know that the sample mean, X ~ N(μ, σ/√n) where μ is the population mean, σ is the population standard deviation, and n is the sample size.

Substituting the given values, we get:

X ~ N(50, 5/√36)

X ~ N(50, 5/6)

Now, we need to find P(X > 50.5), which can be calculated as:

P[X - μ / (σ/√n) > (50.5 - 50) / (5/6)]

P[Z > 0.6]

Using normal distribution tables or calculator, we can find that P[Z > 0.6] = 0.2743.

Therefore, the answer is C.

A Random Sample of Size 36 Is Taken from a Population