Question

18. A population of values has a normal distribution with μ=10.3μ=10.3 and σ=19.5σ=19.5. You intend to draw a random sample of size n=229.

Find the probability that a sample of size n=229 is randomly selected with a mean between 8.5 and 9.
P(8.5 < M < 9) =

Please check your work to make sure its right, i have similar problems like this. I have only 2 chances to get it right

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 = = 10.3

standard deviation = = 19.5

n = 229

=10.3

₌ / n = 19.5229 = 1.2886

P(8.5 < M < 9)

P ( 8.5 - 10.3 / 1.2886) < ( M - / ) < ( 9 - 10.3 /1.2886)

P (-1.8 / 1.2886 < z < -1.3 / 1.2886 )

P (-1.397 < z < - 1.009 )

P ( z < - 1.009 ) - P ( z < -1.397 )

Using z table

= 0.1562 - 0.0823

= 0.0739

Probability = 0.0739