Question

A population of values has a normal distribution with μ=186.2 and σ=5.3 If a random sample of size n=19 is selected,

1. Find the probability that a single randomly selected value is greater than 185.8. Round your answer to four decimals. to find answer
   P(X > 185.8) =
   
2. Find the probability that a sample of size n=19 is randomly selected with a mean greater than 185.8. Round your answer to four decimals. to find answer
   P(M > 185.8) =

Answer 1

Solution :

Given that ,

mean = = 186.2

standard deviation = = 5.3

P(x > 185.8) = 1 - P(x < 185.8)

= 1 - P[(x - ) / < (185.8 - 186.2) / 5.3)

= 1 - P(z < -0.08)

= 1 - 0.4681

= 0.5319

P(x > 185.8) = 0.5319

M = / n = 5.3 / 19 = 1.2159

P(M > 185.8) = 1 - P(M < 185.8)

= 1 - P[(M - M) / M < (185.8 - 186.2) / 1.2159]

= 1 - P(z < -0.33)

= 1 - 0.3707

= 0.6293

P(M > 185.8) = 0.6293