Question

A population of values has a normal distribution with μ=205.2 and σ=9.9 A random sample of size n=169 is drawn.

1. Find the probability that a single randomly selected value is greater than 205.1. Round your answer to four decimal places.
   P(X>205.1)=
   
2. Find the probability that a sample of size n=169 is randomly selected with a mean greater than 205.1. Round your answer to four decimal places.
   P(M>205.1)=

Answer 1

Solution :

Given that ,

mean = = 205.2

standard deviation = = 9.9

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

= 1 - P[(x - ) / < (205.1 - 205.2) / 9.9)

= 1 - P(z < -0.01)

= 1 - 0.496

= 0.5040

P(x > 205.1) = 0.5040

M = / n = 9.9 / 169 = 0.7615

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

= 1 - P[(M - M) / M < (205.1 - 205.2) / 0.7615]

= 1 - P(z < -0.13)

= 1 - 0.4483

= 0.5517

P(M > 205.1) = 0.5517