Question

A population of values has a normal distribution with μ=106.9μ=106.9 and σ=12.3σ=12.3. You intend to draw a random sample of size n=153n=153.

Find the probability that a sample of size n=153n=153 is randomly selected with a mean between 106.8 and 108.7.
P(106.8 < M < 108.7) =

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.

Answer 1

Solution :

Given that,

mean = = 106.9

standard deviation = = 12.3

n = 153

= 106.9

₌ / n = 12.3 153 = 0.9944

P (106.8 < M<108.7 )

P (106.8 - 106.9/ 0.9944 ) < ( M -  / ) < ( 108.7 - 106.9 / 0.9944 )

P ( -0.1 / 0.9944 < z < 1.8 / 0.9944 )

P (-0.100 < z < 1.810 )

P ( z < 1.810 ) - P ( z < -0.100 )

Using z table

= 0.9649 - 0.4602

= 0.5047

Probability = 0.5047