A manufacturer knows that their items have a normally distributed lifespan, with a mean of 12.3 years, and standard deviation of 0.7 years. If you randomly purchase 14 items, what is the probability that their mean life will be longer than 12 years?

The probability is  

Step-by-step explanation:

From the question we are told that

   The  mean is  

    The standard deviation is  

    The sample size is  n = 14

Generally the standard error of the mean is mathematically represented as

=>      

=>      

Generally the probability that their mean life will be longer than 12 years is mathematically represented as

From the z table  the area under the normal curve to the left corresponding to    -0.6034  is

=>    

=>  

distance covered by pamela in 9 l of fuel = 99km

let us apply unitary method here.

distance covered by pamela in 1 l of fuel =99/9 =11 km

now let us find distance covered by pamela if she has 12 l of fuel.

distance covered in 12 l = distance covered in 1 l of fuel * 12

we know that distance covered by here in 1 l is 11 km.

so distance covered in 12 l of fuel = 11*12 = 132 km.

where is the figure