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Chapter 7: Q.97 (page 438)

Certain coins have an average weight of 5.201grams with a standard deviation of 0.065g. If a vending machine is designed to accept coins whose weights range from 5.111g to 5.291g, what is the expected number of rejected coins when 280randomly selected coins are inserted into the machine?

Short Answer

Expert verified

Therefore the probability that accepted coins weights will lies 5.111gram to 5.291gram of randomly selected 280 coins is 1 . Thus, all the coins lie within the given limits.

Step by step solution

01

Given Information

Given in the question that,

the standard deviation of 0.065 g,

02

Explanation

The average weight of coins is 5.201grammes, with a standard variation of 0.065grammes, according to the information provided. To compute the chance that the weights of randomly picked 280coins will range from 5.111grammes to 5.291grammes, use the Ti-83 calculator. To do so, go to 2nd, then DISTR, and then scroll down to the typical CDF option and enter the supplied information. Then, on the calculator, press the ENTER key to get the desired result. Below is an example of a screenshot.

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Most popular questions from this chapter

M&M candies large candy bags have a claimed net weight of 396.9g. The standard deviation for the weight of the

individual candies is 0.017g. The following table is from a stats experiment conducted by a statistics class.

RedOrangeYellowBrownBlueGreen
0.751
0.735
0.883
0.696
0.881
0.925
0.841
0.895
0.769
0.876
0.863
0.914
0.856
0.865
0.859
0.855
0.775
0.881
0.799
0.864
0.784
0.8060.854
0.865
0.966
0.852
0.824
0.840
0.810
0.865
0.859
0.866
0.858
0.868
0.858
1.015
0.857
0.859
0.848
0.859
0.818
0.876
0.942
0.838
0.851
0.982
0.868
0.809
0.873
0.863


0.803
0.865
0.809
0.888


0.932
0.848
0.890
0.925


0.842
0.940
0.878
0.793


0.832
0.833
0.905
0.977


0.807
0.845

0.850


0.841
0.852

0.830


0.932
0.778

0.856


0.833
0.814

0.842


0.881
0.791

0.778


0.818
0.810

0.786


0.864
0.881

0.853


0.825


0.864


0.855


0.873


0.942


0.880


0.825


0.882


0.869


0.931


0.912





0.887

The bag contained 465candies and the listed weights in the table came from randomly selected candies. Count the weights.

a. Find the mean sample weight and the standard deviation of the sample weights of candies in the table.

b. Find the sum of the sample weights in the table and the standard deviation of the sum of the weights.

c. If 465M&Ms are randomly selected, find the probability that their weights sum to at least 396.9.

d. Is the Mars Company鈥檚 M&M labeling accurate?

The length of time a particular smartphone's battery lasts follows an exponential distribution with a mean of ten months. A sample of 64 of these smartphones is taken.

Find the middle 80% for the total amount of time 64 batteries last.

According to the Internal Revenue Service, the average length of time for an individual to complete (keep records for, learn, prepare, copy, assemble, and send) IRS Form 1040is 10.53hours (without any attached schedules). The distribution is unknown. Let us assume that the standard deviation is two hours. Suppose we randomly sample 36taxpayers.

a. In words, 围=_____________

b. In words,X=_____________

c. X炉~_____(_____,_____)

d. Would you be surprised if the 36taxpayers finished their Form 1040s in an average of more than 12hours? Explain why or why not in complete sentences.

e. Would you be surprised if one taxpayer finished his or her Form 1040in more than 12hours? In a complete sentence, explain why.

Cans of a cola beverage claim to contain 16 ounces. The amounts in a sample are measured and the statistics are n=34,x炉=16.01ounces. If the cans are filled so that 渭=16.00ounces (as labeled) and 蟽=0.143ounces, find the probability that a sample of 34 cans will have an average amount greater than 16.01ounces. Do the results suggest that cans are filled with an amount greater than 16 ounces?

Men have an average weight of 172pounds with a standard deviation of 29pounds.

a. Find the probability that 20randomly selected men will have a sum weight greater than 3600lbs.

b. If 20 men have a sum weight greater than 3500lbs, then their total weight exceeds the safety limits for water taxis. Based on (a), is this a safety concern? Explain.
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