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

=>    

=>  

-1, -2, -3, -4, -6

step-by-step explanation:

r(0,90)(x,y) . t(-5,0)

last option

step-by-step explanation:

∆def to ∆d"e"f"

- rotate 90 counterclockwise degrees

- then translated 5 to the left (x --> x - 5)

answer is the last option