Question

A population of values has a normal distribution with μ = 109.2 and σ = 65.6 . You intend to draw a random sample of size n = 90 .

Find the probability that a sample of size n = 90 is randomly selected with a mean greater than 96.1. P( ¯ x > 96.1) =

Enter your answers as numbers accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted. License

Answer 1

Solution :

Given that ,

mean = = 109.2

standard deviation = = 65.6

n = 90

= = 109.2 and

= / n = 65.6 / 90 = 6.9148

P( > 96.1) = 1 - P( < 96.1)

= 1 - P(( - ) / < (96.1 - 109.2) / 6.9148)

= 1 - P(z < -1.894)

= 1 - 0.0291 Using standard normal table.

= 0.9709

The probability that a sample of size n = 90 is randomly selected with a mean greater than 96.1 is 0.9709.