Question

A consumer price analyst claims that prices for liquid crystal display (LCD) computer monitors have a mean of $200 and a standard deviation of $48.

1. What is the probability that a randomly selected LCD computer monitor costs less than $210? Assume here that the prices are normally distributed

2. You randomly selected 25 LCD compute monitors. What is the probability that their mean cost is less than $210? Assume here that the prices are normally distributed

3. You randomly selected 64 LCD compute monitors. What is the probability that their mean cost is less than $210?

Answer 1

a)

Given,

= 200 , = 48

We convert this to standard normal as

P(X < x) = P( Z < ( x - ) / )

So,

P(X < 210) = P(Z < (210 - 200) / 48)

= P(Z < 0.21)

= 0.5832 (From Z table)

b)

Using central limit theorem,

P( < x) = P(Z < ( x - ) / ( / sqrt(n) )

So,

P( < 210) = P(Z < ( 210 - 200) / (48 / sqrt(25) ) )

= P(Z < 1.04)

= 0.8508 (From Z table )

c)

P( < 210) = P(Z < ( 210 - 200) / (48 / sqrt(64) ) )

= P(Z < 1.67)

= 0.9525 (From Z table )