Question

A population of values has a normal distribution with μ = 118.4 μ = 118.4 and σ = 87.7 σ = 87.7 . You intend to draw a random sample of size n = 24 n = 24 .

Find the probability that a single randomly selected value is less than 62.9. P(X < 62.9) = ______

Find the probability that a sample of size n = 24 n = 24 is randomly selected with a mean less than 62.9. P(M < 62.9) = ______

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 ,

a) P(x < 62.9)

= P[(x - ) / < (62.9 - 118.4) / 87.7 ]

= P(z < -0.633 )

Using z table,

= 0.2634

b) = 118.4

= / n = 87.7 / 24 = 17.902

P(M < 62.9) = P((M - ) / < (62.9 - 118.4) /17.902 )

= P(z < -3.100)

Using z table

= 0.0010