Question

Suppose that a population is known to be normally distributed with μ =2,400 and σ=220. If a random sample of size n=88 is​ selected, calculate the probability that the sample mean will exceed 2,500

​P(x > 2,500​)=

​(Round to four decimal places as​ needed.)

Answer 1

Solution :

Given that ,

mean = = 2,400

standard deviation = = 220

n = 88

= 2,400

= / n = 220/ 88 = 23.45

P( > 2,500) = 1 - P( < 2,500)

= 1 - P[( - ) / < (2,500 - 2,400) / 23.45]

= 1 - P(z < 4.26)

    Using standard normal table,

P( >2500) = 1 - 1

Probability = 0