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The Acme Company manufactures widgets. The distribution ofwidget weights is bell-shaped. The widget weights have a mean of 44ounces and a standard deviation of 9 ou...

Question

The Acme Company manufactures widgets. The distribution ofwidget weights is bell-shaped. The widget weights have a mean of 44ounces and a standard deviation of 9 ounces. Use the StandardDeviation Rule, also known as the Empirical Rule. Suggestion:sketch the distribution in order to answer these questions. a) 68%of the widget weights lie between and b) What percentage of thewidget weights lie between 17 and 53 ounces? % c) What percentageof the widget weights lie above 26 ?

The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 44 ounces and a standard deviation of 9 ounces. Use the Standard Deviation Rule, also known as the Empirical Rule. Suggestion: sketch the distribution in order to answer these questions. a) 68% of the widget weights lie between and b) What percentage of the widget weights lie between 17 and 53 ounces? % c) What percentage of the widget weights lie above 26 ?



Answers

Express all z scores with two decimal places. Plastic Waste Data Set 31 "Garbage Weight" in Appendix B lists weights (ib) of plastic discarded by households. The highest weight is 5.28 Ib, the mean of all of the weights is $\bar{x}=$ 1.911 Ib, and the standard deviation of the weights is $s=1.065$ lb. a. What is the difference between the weight of 5.28 Ib and the mean of the weights? b. How many standard deviations is that [the difference found in part (a)]? c. Convert the weight of 5.28 lb to a $z$ score. d. If we consider weights that convert to $z$ scores between -2 and 2 to be neither significantly low nor significantly high, is the weight of 5.28 ib significant?

Welcome to enumerate in the current problem. It is given that the weight of semen bags wreaks off cement bags are distributed Normally, cement bags follow normal distribution with means 60 lb and sigma one lb. Okay. No, we have to use the empirical rule. Okay, so using empirical rule to find the probability that this x this X lie between 56 58. L. Bay too 62. Okay, so that means the availability of 58 2 X 2 62. How much will this from listening? Now? We will again take the path of standardization forest or it's sort of standardized? Simply, we can rather going for standardizing approach. We will take the empirical approach. Right? So we will have a normal distribution like this which is centered at 60 and has a standard deviation of 1 30 61 this is 62 this is 63 and again this is 6 59 this is 58 this is 57. So this is two sigma limit, 6 58 to 62. This is nothing but two sigma limit and two sigma limit contains 95% of the entire population, so this is 95% of the cement bags would weigh between between 58 lb to 60 to 80.

Welcome to New Madrid. In the current problem, we are given that the weights of swimming bags, which follows a normal distribution with mean 60 and sigma's one. What will be the probability of the semen bags to win more than 62 L. D. You asked now if it really remember it correctly, the probability that the entire distribution will groups will be will contain within two sigma limit will be 95%. So this is here 2.5% and this is here it is 2.5%. So probability that it will exceed 62 is this area. Therefore it is 2.5% from the empirically love.

Welcome to new Madrid. In the current problem we are given that X. The variable is weight off semen bags. Okay. And the units are in L. B. Now it is given that X follows a normal distribution with mean 60 MB. And sigma is supposed to from anything that means what if we had incorporated a normal curve over here then for example this so in that case this in the middle we will have 60 then one sigma distance will be one. So that will be 60 plus one, next will be 62 next will be 60 ft and here it will be 59. This meant this will be 58 this would be 15 7. Now the question we are asked that what is the probability that the and of course using empirical room. Okay, so here we are going to use her empirical rules according to which probability that X lies between meal plus sigma plus minus sigma. There will be 68% and X lying between new plus minus two sigma will be 95% and X line between new plans, Ministry sigma will be 99%. Okay, so now in this question they're asking what is it person date of bags that will weigh between 59? Yeah to 61 Right? The probability that X lies between X two 61 would be nothing but one sigma. Distin's correct because the mean if it is at 60 plus one will be 61 minus one or one sigma would be $50. So whatever we consider in terrible we are considering that is one sigma distance correct. And that shows that books this will have 68% of the data. So the probability is 68%.


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