Question

Suppose X a population has a distribution that is skewed to the right and µ =400 and σ =24. If a random sample of size 144 is drawn from the population: (Show work)

a) What is the name of theorem that allows us to solve this problem? ___________

b) What is the reason that we use that theorem in this case? ___________

c) Compute P( > 398) ___________ In part c, is the sample mean.

Answer 1

Solution :

Given that,

mean = = 400

standard deviation = = 24

n = 144

a) Central Limit Theorem

b) because sample size greater than or equal 30

= = 400

= / n = 24/ 144 = 2

c) P( > 398) = 1 - P( < 398)

= 1 - P[( - ) / < (398 - 400) /2 ]

= 1 - P(z < -1.00)

Using z table,    

= 1 - 0.1587

= 0.8413