Can you help solve this normal probability distribution problem?

Question

Mean life a refrigerator follows a Normal Distribution with a mean of 7.2 years and a standard deviation of 1.9 years. What fraction of the refrigerator last more than 10 Years? Can you explain how you come up with your answer?

Answer 1

Dear shavon60120,

When solving this type of problem, you need to either have a calculator that gives you values from the normal distribution or look them up in tables. Tables are usually standardized, meaning they are for a normal distribution with a mean of 0 and a standard deviation of 1.

If you are using standardized normal tables, you can put the numbers in your problem into standardized form by shifting and rescaling the particular normal distribution you start with. This is done by first subtracting the mean from your quantity of interest (this does the shifting), and then dividing this result by the standard deviation (this does the rescaling). Thus, for your problem, where x = 10 years is your quantity of interest, m = 7.2 years is the mean, and d = 1.9 years is the standard deviation, you get

z = (x - m) / d
= (10 - 7.2) / 1.9
= 2.8 / 1.9
= 1.47368 (to five decimal places).

The quantity z now represents the number of standard deviations that your quantity is above the mean. (If z had been negative, it would represent the number of standard deviations below the mean.) In other words, z gives you the same number of standard deviations above the mean for a standard normal distribution that x gave you in your original distribution.

At this point you should find the probability in a standard normal table that corresponds to 1.47368 standard deviations (typically shown as the lowercase Greek letter sigma). Recall that the probability of being less than or equal to the mean for a normal distribution is 0.5 because the distribution is symmetric about its mean, so for values above the mean the probability you find should be greater than 0.5 (essentially, the probability you are finding is equal to the area under the normal density curve up to your quantity of interest).

I find the probability is 0.92972 (to five decimal places) that you would be below 1.47368 standard deviations. This probability is the same for the life of a refrigerator being no more than 10 years. However, since you want to know the chance of a refrigerator lasting more than 10 years, you need to subtract the probability just obtained from 1.

Therefore, the probability of a refrigerator lasting more than 10 years is

1 - 0.92972 = 0.07028 (to five decimal places).

Answer 2

you're able to desire to calculate the z-center of the cost first, it incredibly is given by ability of z = ( 12 - ? ) / ? From there you could the two seek for the prospect linked with that z-score in common statistical tables or use a typical equation to calculate the prospect. many times you would be finding up in tables while you're in basic terms now discovering approximately this; the formula is a sprint too complicated.