Question

Based on past experience, a bank believes that 14% of the people who receive loans will not make payments on time. The bank has recently approved 500 loans. Answer the following questions. a) What are the mean and standard deviation of the proportion of clients in this group who may not make timely payments? Î¼p = 0.14 SDp = 0.012 (Round to three decimal places as needed.) b) What assumptions underlie your model? Are the conditions met? A. With reasonable assumptions about the sample, all the conditions are met. B. The randomization condition is not met. C. The success/failure condition is not met. D. The 10% and success/failure conditions are not met. E. The randomization and 10% conditions are not met. F. The randomization and success/failure conditions are not met. G. The 10% condition is not met. H. Without unreasonable assumptions, none of the conditions are met. c) What is the probability that over 16% of these clients will not make timely payments? Pp > 0.16 = 0.091 (Round to three decimal places as needed.)

          Based on past experience, a bank believes that 14% of the people who receive loans will not make payments on time. The bank has recently approved 500 loans. Answer the following questions.

a) What are the mean and standard deviation of the proportion of clients in this group who may not make timely payments?
Î¼p = 0.14
SDp = 0.012
(Round to three decimal places as needed.)

b) What assumptions underlie your model? Are the conditions met?
A. With reasonable assumptions about the sample, all the conditions are met.
B. The randomization condition is not met.
C. The success/failure condition is not met.
D. The 10% and success/failure conditions are not met.
E. The randomization and 10% conditions are not met.
F. The randomization and success/failure conditions are not met.
G. The 10% condition is not met.
H. Without unreasonable assumptions, none of the conditions are met.

c) What is the probability that over 16% of these clients will not make timely payments?
Pp > 0.16 = 0.091
(Round to three decimal places as needed.)

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Added by Austin O.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Ana Carolina Da Cruz

03/11/2023

Step 1

Mean (μp) = p = 0.14 (given) Standard Deviation (SDp) = sqrt(p * (1-p) / n) = sqrt(0.14 * (1-0.14) / 500) Now, let's calculate the values: μp = 0.14 SDp = sqrt(0.14 * 0.86 / 500) = 0.017 So, the mean and standard deviation are: μp = 0.14 SDp = 0.017 Now, Show more…

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Based on past experience, a bank believes that 14% of the people who receive loans will not make payments on time. The bank has recently approved 500 loans. Answer the following questions. a) What are the mean and standard deviation of the proportion of clients in this group who may not make timely payments? Î¼p = 0.14 SDp = 0.012 (Round to three decimal places as needed.) b) What assumptions underlie your model? Are the conditions met? A. With reasonable assumptions about the sample, all the conditions are met. B. The randomization condition is not met. C. The success/failure condition is not met. D. The 10% and success/failure conditions are not met. E. The randomization and 10% conditions are not met. F. The randomization and success/failure conditions are not met. G. The 10% condition is not met. H. Without unreasonable assumptions, none of the conditions are met. c) What is the probability that over 16% of these clients will not make timely payments? Pp > 0.16 = 0.091 (Round to three decimal places as needed.)

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Transcript

00:01 In this question, we are assuming here that a bank believes that 14 % of the people who receive loans will not make payments on time.

00:09 So this means that the proportion here is 014.

00:13 So now, if we consider that they made a number of 100, 500 loans here recently, and we can assume that each person will go there independently from the other to get a loan, and then, of course, independently from the other, the bank will decide if it will give the loan or not, right? so we can assume here that we have some kind of independence between each person, okay? so now, why i'm saying this? because in letter b, we are going to see why.

00:52 In item a, we should find what is the mean in the standardization of the proportion.

00:57 So when we are working with proportions here, the mean of the proportion is the same as the proportion in what we believe in the population.

01:06 So in this case would be this 014.

01:08 The standard deviation of the proportion is given by this means 014 times 1 minus this value divided by the total number of observations.

01:20 Okay.

01:22 So this means that the standard deviation 0 .016.

01:26 So now with this information, first we need to find if the conditions are all not.

01:32 So in this case here we should check if you have independent.

01:35 So basically we can assume that the bank will like treat each person independently from the other.

01:42 So independent is okay.

01:44 So this means that the randomization is okay.

01:47 So this is what means to be randomized here.

01:52 Like these five loans here are independent.

01:56 Then the other thing that we should check is like if you're in this case checking, to compute this proportion here, if you're checking if that person paid or not pay on time.

02:08 So we have only two possibilities.

02:10 We have this success, which is, in this case, that the person did not pay on time, and the failure.

02:16 So basically, the information that we are collecting out of this 500 is basically yes or no...

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