Question

A population of values has a normal distribution with μ=87.3μ=87.3 and σ=50.4σ=50.4. You intend to draw a random sample of size n=13n=13.

Find P₆₈, which is the score separating the bottom 68% scores from the top 32% scores.
P₆₈ (for single values) =

Find P₆₈, which is the mean separating the bottom 68% means from the top 32% means.
P₆₈ (for sample means) =

Answer 1

Solution :

Given that,

Solution :

Given that,

mean = = 87.3

standard deviation = = 50.4

n = 13

=87.3

₌ / n = 50.4 13 =13.9784

Using standard normal table,

P( Z < z) = 68%
P(Z < z) = 0.68

z = 0.47

Using z-score formula,

= z * +

= 0.47 * 13.9784 + 87.3

= 93.86

P₆₈ = 94

Using z-score formula,

= z * +

= 0.47 * 13.9784 + 87.3

= 93.86

= 93.9