Question

A population of values has a normal distribution with μ=199.9μ=199.9 and σ=45.2σ=45.2. You intend to draw a random sample of size n=111n=111.

Find the probability that a single randomly selected value is greater than 200.3.
P(X > 200.3) =

Find the probability that a sample of size n=111n=111 is randomly selected with a mean greater than 200.3.
P(¯xx¯ > 200.3) =  Enter your answers as numbers accurate to 4 decimal places.

Answer 1

Solution:-

μ = 199.9 and σ = 45.2

a) The probability that a single randomly selected value is greater than 200.3 is 0.4965.

x = 200.3

By applying normal distribution:-

z = 0.00885

Use the z-score table or p-value calculator.

P(z > 0.0085) = 0.4965

b) The probability that a sample of size n=111 is randomly selected with a mean greater than 200.3 is 0.4629.

x = 200.3

By applying normal distribution:-

z = 0.0932

Use the z-score table or p-value calculator.

P(z > 0.0932) = 0.4629