Question

Find the indicated probability assuming that x is a random variable with a normal distribution with the given mean and standard deviation. (Round your answer to four decimal places.)

P(95 ≤ x ≤ 307), μ = 20, σ = 100

Answer 1

Solution :

Given that ,

mean = = 20

standard deviation = = 100

= P[(95 - 20 /100 ) (x - ) / (307 - 20 / 100) ]

= P(0.75 z 2.87)

= P(z 2.87) - P(z 0.75 )

= 0.9979 - 0.7734

= 0.2245

P(95 ≤ x ≤ 307) = 0.2245