Question

A recent market indicated a typical family of four spends $490 per month on food. Assume the distribution of food expenditure for a family of four follows the normal distribution with a standard deviation of $80 per month. a. What percent of the families spend less than $430 per month on food? Answer: 22.66% (answer in 2 digits decimal) b. What percent of the families spend more than $430 but less than $490 per month on food? Answer: 27.34 % (answer in 2 digits decimal) c. What percent of the families spend more than $500 per month on food? Answer: 45.02 % (answer in 2 digits decimal) d. How much does a family of four minimum spending, to be the 20% of the families with the highest spending on food? Answer: $ 20 % (answer in 2 digits decimal) e. What is the maximum food expenditure of the lowest 15% families? Answer: $ 406.80% (answer in 2 digits decimal)

          A recent market indicated a typical family of four spends $490 per month on food. Assume the distribution of food expenditure for a family of four follows the normal distribution with a standard deviation of $80 per month.
a. What percent of the families spend less than $430 per month on food?
Answer: 22.66% (answer in 2 digits decimal)
b. What percent of the families spend more than $430 but less than $490 per month on food?
Answer: 27.34 % (answer in 2 digits decimal)
c. What percent of the families spend more than $500 per month on food?
Answer: 45.02 % (answer in 2 digits decimal)
d. How much does a family of four minimum spending, to be the 20% of the families with the highest spending on food?
Answer: $ 20 % (answer in 2 digits decimal)
e. What is the maximum food expenditure of the lowest 15% families?
Answer: $ 406.80% (answer in 2 digits decimal)

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A recent market indicated a typical family of four spends 490 per month on food. Assume the distribution of food expenditure for a family of four follows the normal distribution with a standard deviation of80 per month.
a. What percent of the families spend less than 430 per month on food?
Answer: 22.66% (answer in 2 digits decimal)
b. What percent of the families spend more than430 but less than 490 per month on food?
Answer: 27.34 % (answer in 2 digits decimal)
c. What percent of the families spend more than500 per month on food?
Answer: 45.02 % (answer in 2 digits decimal)
d. How much does a family of four minimum spending, to be the 20% of the families with the highest spending on food?
Answer: 20 % (answer in 2 digits decimal)
e. What is the maximum food expenditure of the lowest 15% families?
Answer: 406.80% (answer in 2 digits decimal)

Added by Jennifer C.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Madhur L

06/13/2023

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Step 1: We are given that the average food expenditure for a family of four is $490 per month and the standard deviation is $80 per month. Show more…

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A recent market indicated a typical family of four spends $490 per month on food. Assume the distribution of food expenditure for a family of four follows the normal distribution with a standard deviation of $80 per month. a. What percent of the families spend less than $430 per month on food? Answer: 22.66% (answer in 2 digits decimal) b. What percent of the families spend more than $430 but less than $490 per month on food? Answer: 27.34 % (answer in 2 digits decimal) c. What percent of the families spend more than $500 per month on food? Answer: 45.02 % (answer in 2 digits decimal) d. How much does a family of four minimum spending, to be the 20% of the families with the highest spending on food? Answer: $ 20 % (answer in 2 digits decimal) e. What is the maximum food expenditure of the lowest 15% families? Answer: $ 406.80% (answer in 2 digits decimal)

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Transcript

00:01 Hello students, in this question we have four parts.

00:07 First of all we have to draw the diagram.

00:14 So this is mu.

00:16 Mu equal to 490 and sigma equal to 90.

00:26 So now first one is that probability of 30 less than or equal to x less than 490.

00:36 So it is equal to probability of minus 5 .11 less than z less than 0.

00:45 We take x as 490.

00:49 So here 490 x minus mu.

00:52 But we know that this formula z equal to x minus mu by sigma.

00:57 So we have to substitute 30 minus 490 by standard deviation 90.

01:02 We got minus 5 .11 less than z x minus mu by sigma z.

01:08 Here 490 minus 490 is 0.

01:11 So note that it is 0 .5 minus 0.

01:22 That is equal to 0 .5.

01:25 Means 50 % probability.

01:28 So it is a 50 % probability.

01:30 And now the second one.

01:32 Second one is p of x less than 430.

01:36 So it is equal to p of z less than minus 0 .67.

01:41 It is equal to 0 .2514.

01:47 It is equal to 25 .14%.

01:51 Here it is equal to p of x minus mu by sigma less than 430 minus 490 divided by 90.

02:04 So it is equal to x minus mu by sigma z...

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