Stats Homework Help Please?

A candy bar takes an average of 3.4 hours to move through an assembly line. If the standard deviation is 0.5 hours, what is the probability that the candy bar will take between 3 and 4 hours to move through the line?






The average noise level in a diner is 30 decibels with a standeard deviation of 6 deviation of 6 decibels. 99% of the time, the noise level is below what value?






The mean income per household in a certain state is $29,500 with a standard deviation of $5,750. The middle 95% of income is between what two values? The incomes are normally distributed.

$23,750 and $35,250

$18,000 and $41,000

$29,500 and $41,000

$12,250 and $46,750

$12,325 and $81,550


First question: In these situations it's very helpful to draw a bell-shaped curve to help you see which variables to enter into your calculator.

You have to calculate the probability that it'll take the candy bar no longer than 4 and no shorter than 3 hours to be assembled. So your left value is 3 and your right value is 4. You already know the average and the standard deviation. This gives you normalcdf(3,4,3.4,0.5) = 0.6731.

Second question: Draw a bell-shaped curve for yourself! You have to use the area below the graph to calculate the value you are looking for. The surface below the entire bell-shape equals 1; the surface of 99% will then be 0.99. You're looking for the 99% lowest noise levels, so this is the left side of the graph and this means that you may use invNorm. invNorm(0.99, 30, 6) = 43.96

Third question: You should learn the normal distribution values by heart, they come in very handy. Because these values on the far right and left of the curve both equal 2.5, you can easily calculate the solution to this problem. Use invNorm to calculate your left value (remember that with invNorm you can only use surface areas to the left of the value you're calculating!): invNorm(0.025, 29500, 5750) = 18210. then comes your right value: invNorm(0.975, 29500, 5760) = 40679. Round these numbers off and there's your answer.

I hope my explanation was clear- while I speak English fluently it isn't my first language and my mathematical vocabulary isn't that extensive.