Question

A population of values has a normal distribution with μ=6.8 and σ=53. A random sample of size n=197 is drawn.

1. Find the probability that a single randomly selected value is between 4.5 and 17. Round your answer to four decimal places. to find answer
   P(4.5<X<17)=
2. Find the probability that a sample of size n=197 is randomly selected with a mean between 4.5 and 17. Round your answer to four decimal places. to find answer
   P(4.5<M<17)=  

Answer 1

Solution :

Given that ,

mean = = 6.8

standard deviation = = 53

P(4.5 < x < 17) = P[(4.5 - 6.8)/ 53) < (x - ) /  < (17 - 6.8) / 53) ]

= P(-0.04 < z < 0.19)

= P(z < 0.19) - P(z < -0.04)

= 0.5753 - 0.484

= 0.0913

P(4.5 < x < 17) = 0.0913

n = 197

M = 6.8

M = / n = 53 / 197 = 3.7761

P(4.5 < M < 17) = P((4.5 - 6.8) / 3.7761< (M - M) / M < (17 - 6.8) / 3.7761)

= P(-0.61 < Z < 2.70)

= P(Z < 2.70) - P(Z < -0.61)

= 0.9965 - 0.2709

= 0.7256

P(4.5 < M < 17) = 0.7256