Question

A population of values has a normal distribution with μ=5.1μ=5.1 and σ=71.6σ=71.6. You intend to draw a random sample of size n=112n=112.

Find the probability that a single randomly selected value is between -15.9 and -13.2.
P(-15.9 < X < -13.2) =

Find the probability that a sample of size n=112n=112 is randomly selected with a mean between -15.9 and -13.2.
P(-15.9 < M < -13.2) =

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 :

a ) Given that,

mean = = 5.1

standard deviation = = 71.6

n = 112

= 5.1

= / n =71.6 112 = 6.7656

P(-15.9 < X < -13.2)

P ( -15.9 - 5.1 / 6.7656) < ( - /) < ( -13.2 - 5.1 / 6.7656)

P ( - 21 / 6.7656 < z < -18.3 / 6.7656 )

P (-3.104 < z < -2.705)

P ( z < -2.705 ) - P ( z < -3.104)

Using z table

= 0.0034 - 0.0010

= 0.0024

Probability = 0.0024