The length of life of an instrument produced by a machine has a normal distribution with a mean of 12 months and standard deviation of 2 months. find the probability that an instrument produced by this machine will last a) less than 7 months b) between 7 and 12 months.

a) 0.0062

b) 0.4938

Step-by-step explanation:

a)

We need to convert each to z score and use z-table to find the probabilities.

The formula for z score is:

Where is the mean (given as 12), and

 is the standard deviation (given as 2)

So we have:

Hence, probability is 0.0062

b)

Here, we want between 7 and 12, we already found z-score of x = 7 to be -2.5. Let's find z score of x = 12 using the formula:

So we have:

Hence, probability is 0.4938

t = 3

step-by-step explanation:

put t = 3 in this expression :

(3²-1)(3²-2)(3² - 3)(3² - 4) = 8×7×6×5 = 56×30 = 1680

its 50 miles away from the starting point