Question

Heights of fences are normally distributed with a mean of 52 inches and a standard deviation of 4 inches.

1. Find the probability that one randomly selected fence is under 54 inches.

2. Find the probability that two randomly selected fences are both under 54 inches.

3. Find the probability that the mean height of 4 randomly selected fences is under 54 inches.

Answer 1

Solution :

Given that ,

1) P(x < 54)

= P[(x - ) / < (54 - 52) / 4 ]

= P(z < 0.5)

Using z table,

= 0.6915

2) Given that ,

= 52

= / n = 4/ 2 = 2.83

P( < 54) = P(( - ) / < (54 - 52) / 2.83)

= P(z < 0.71)

Using z table

= 0.7611

3) Given that ,

= 52

= / n = 4/ 4 = 2

P( < 54) = P(( - ) / < (54 - 52) / 2)

= P(z < 0.71)

Using z table

= 0.9772