Question

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 12.5 years, and standard deviation of 0.9 years. If you randomly purchase one item, what is the probability it will last longer than 11 years? Round answer to three decimal places

Answer 1

Solution :

Given that,

mean = = 12.5

standard deviation = = 0.9

n=1

= =12.5

= / n = 0.9 / 1 = 0.9

P( > 11) = 1 - P( < 11)

= 1 - P[( - ) / < (11-12.5) /0.9 ]

= 1 - P(z <-1.67 )

Using z table

= 1 - 0.0475

= 0.9525

probability= 0.9525