Question

Part 1

A manufacturer knows that their items have a normally distributed length, with a mean of 17.3 inches, and standard deviation of 4.3 inches.

If one item is chosen at random, what is the probability that it is less than 26.5 inches long?

Part 2

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 13.2 years, and standard deviation of 0.9 years.

If you randomly purchase one item, what is the probability it will last longer than 12 years?

Answer 1

Solution :

Given that ,

1) mean = = 17.3

standard deviation = = 4.3

P(x < 26.5) = P[(x - ) / < (26.5 - 17.3) / 4.3]

= P(z < 2.14)

Using z table,

= 0.9838

2) Given that ,

mean = = 13.2

standard deviation = = 0.9

P(x > 12) = 1 - p( x< 12)

=1- p P[(x - ) / < (12 - 13.2) / 0.9 ]

=1- P(z < -1.33)

Using z table,

= 1 - 0.0918

= 0.9082