A manufacturer knows that their items have a normally distributed lifespan, with a mean of 13.9 years, and standard deviation of 2.9 years. If you randomly purchase 9 items, what is the probability that their mean life will be longer than 14 years

0.4588

Step-by-step explanation:

When we have random sample, the z score formula we use is:

z = (x-μ)/σ/√n

where x is the raw score = 14

μ is the population mean = 13.9

σ is the population standard deviation = 2.9

n is random number of samples = 9

z = 14 - 13.9/2.9/√9

z = 0.1/2.9/3

z = 0.10345

Probability value from Z-Table:

P(x<14) = 0.5412

P(x>14) = 1 - P(x<14) = 0.4588

The probability that their mean life will be longer than 14 years is 0.4588

d. bc = 12 and ef = 16

step-by-step explanation:

we are given that δabc : δdef such that .

also, it is given that

so, from the options, we need that .

a.

b.

c.  

d.

as, we can see that only option d gives the same ratio as i.e. .

hence, the possible lengths are bc = 12 and ef = 16.