Statistic Help: Probabilty Distribution z-scores?

Question

I need help working out this problem. Someone please explain if you know about probability distribution.

The question:

The weight of items produced by a machine is Normally distributed with a mean of 8 ounces and a standard deviation of 2 ounces.

What is the probability that a randomly selected item will weigh less than 6 ounces?

I NEED HELP. Explain how you work to get the answer.

thanks

Answer 1

P(X<6) = Probability that X is less than 6
Transform the X value of 6 to Z

Z= 6 - 8 / 2 = -2/2 = -1

Look up the Z value of -1 in the standard normal table and we get a probability of 0.1587 or 15.87%.

I think this is right.

Answer 2

When you think of distribution, start with the middle or 50% percentile. The first SD is either +34 or -34% from 50%. Thus, 6 is -1 SD from 8, or put you at 16% (50-34). The 16% is also the chance that you will randomly select 6 ounces.

Answer 3

I knew how to do this back in the 70s.

Mean is 8, std dev is 2, so for the item to weigh less than 6 oz you are under the curve to the left of the mean by more than one std deviation.

So solve for the probability that you will me more than one std away from the mean but only on the left side. That's 1/2 of the probability of being more than one std deviation away from the mean on either side, since the normal distribution is symmetrical around the mean.

There you go, everything but the answer. Come on, somebody else finish this so I can plagiarize the answer.

Answer 4

Don S is right