Question

A population of values has a normal distribution with μ=198.1 and σ=68.8. You intend to draw a random sample of size n=118.

Find the probability that a single randomly selected value is greater than 205.1.
P(X > 205.1) =

Find the probability that a sample of size n=118 is randomly selected with a mean greater than 205.1.
P(M > 205.1) =

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 = = 198.1

standard deviation = = 68.8

a)

P(x > 205.1) = 1 - P(x < 205.1)

= 1 - P[(x - ) / < (205.1 - 198.1) / 68.8]

= 1 - P(z < 0.102)

= 1 - 0.5406

= 0.4594

Probability = 0.4594

b)

M = / n = 68.8 / 118 = 6.3336

P(M > 205.1) = 1 - P(M < 205.1)

= 1 - P[(M - M ) / M < (205.1 - 198.1) / 6.3336]

= 1 - P(z < 1.105)

= 1 - 0.8654

= 0.1346

Probability = 0.1346