A machine manufactures tires with a tread thickness that is...

A machine manufactures tires with a tread thickness that is normally distributed with mean 9.6 millimeters (mm) and standard deviation 2.2 mm. In the problems below, if necessary round to 3 decimal places. (a) What proportion of tires will have a tread above 7.9mm? Points possible: 4 Question 2 (b) The middle 83% of tire thicknesses will be between (lower) mm and (upper) mm. Points possible: 4 Question 3 (c) An independent random sample of 4 tires is made. The sample mean, as a random variable, has expected value mm and standard error mm.

Transcript

00:01 So in this case we have a standard deviation of 0 .16 and a mean of 22 .7 in a normally distributed situation.

00:09 So it doesn't say anywhere that is normally distributed, but because it's measurements usually these are.

00:18 So we can assume that these are.

00:20 So probably before in the problem they tell about this.

00:24 So the mean is 22 .7 and the standard deviation is 0 .16.

00:32 Both in millimeters.

00:37 So what we want to know is what is the probability the tire will be too narrow.

00:41 The tire will be too narrow if it's they say less than 22 .6 so 22 .6 is going to be here and we want to know this probability right here.

00:55 And so to do that we can use a graphical calculator.

00:59 You can do it with tables too but graphical calculator is easier.

01:04 So here we have a ti84 which is a very popular high school calculator with a good statistical module so here we want to go to the distributions so let's clear the screen go to distributions second distributions and we want to find areas of a normal distribution we use the normal cdf number two here the normal cdf so here we put the bounds of the area in this case the green area the left bound the lower bound is all the way to minus infinity so we have to write minus infinity but this calculator you cannot write minus infinity so just put a big number like this that's fine the upper bound is 22 .6 22 .6 and the mean is 22 .70 and the standard deviation is 0 .16 so oops 0 .16 we make so everything is nice and now we paste and we calculate so the probability how many decimal places do they need four decimal places.

02:17 So it's going to be 2660.

02:20 0 .2660.

02:26 0 .0...

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