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. to find answer
   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. to find answer
   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)

Using z table

= 1 -  0.4960

probability= 0.5040

b.

M= = = 205.2

= / n = 9.9 / 169 = 0.76

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

= 1 - P[(M - ) / < (205.1-205.2) /0.76 ]

= 1 - P(z < -0.13)

Using z table

= 1 - 0.4483

= 0.5517

probability= 0.5517