# 7.6 Homework  (Page 2/4)

 Page 2 / 4

Suppose that the duration of a particular type of criminal trial is known to have a mean of 21 days and a standard deviation of 7 days. We randomly sample 9 trials.

• In words, $\mathrm{\Sigma X}=$
• $\mathrm{\Sigma X}\text{~}$
• Find the probability that the total length of the 9 trials is at least 225 days.
• 90 percent of the total of 9 of these types of trials will last at least how long?
• The total length of time for 9 criminal trials
• $N\left(189,21\right)$
• 0.0432
• 162.09

According to the Internal Revenue Service, the average length of time for an individual to complete (record keep, learn, prepare, copy, assemble and send) IRS Form 1040 is 10.53 hours (without any attached schedules). The distribution is unknown. Let us assume that the standard deviation is 2 hours. Suppose we randomly sample 36 taxpayers.

• In words, $X=$
• In words, $\overline{X}=$
• $\overline{X}\text{~}$
• Would you be surprised if the 36 taxpayers finished their Form 1040s in an average of more than 12 hours? Explain why or why not in complete sentences.
• Would you be surprised if one taxpayer finished his Form 1040 in more than 12 hours? In a complete sentence, explain why.

Suppose that a category of world class runners are known to run a marathon (26 miles) in an average of 145 minutes with a standard deviation of 14 minutes. Consider 49 of the races.

Let $\overline{X}=$ the average of the 49 races.

• $\overline{X}\text{~}$
• Find the probability that the runner will average between 142 and 146 minutes in these 49 marathons.
• Find the 80th percentile for the average of these 49 marathons.
• Find the median of the average running times.
• $N\left(\text{145},\frac{\text{14}}{\sqrt{\text{49}}}\right)$
• 0.6247
• 146.68
• 145 minutes

The attention span of a two year-old is exponentially distributed with a mean of about 8 minutes. Suppose we randomly survey 60 two year-olds.

• In words, $X=$
• $X\text{~}$
• In words, $\overline{X}=$
• $\overline{X}\text{~}$
• Before doing any calculations, which do you think will be higher? Explain why.
• the probability that an individual attention span is less than 10 minutes; or
• the probability that the average attention span for the 60 children is less than 10 minutes? Why?
• Calculate the probabilities in part (e).
• Explain why the distribution for $\overline{X}$ is not exponential.

Suppose that the length of research papers is uniformly distributed from 10 to 25 pages. We survey a class in which 55 research papers were turned in to a professor. The 55 research papers are considered a random collection of all papers. We are interested in the average length of the research papers.

• In words, $X=$
• $X\text{~}$
• ${\mu }_{X}=$
• ${\sigma }_{X}=$
• In words, $\overline{X}=$
• $\overline{X}\text{~}$
• In words, $\mathrm{\Sigma X}=$
• $\mathrm{\Sigma X}\text{~}$
• Without doing any calculations, do you think that it’s likely that the professor will need to read a total of more than 1050 pages? Why?
• Calculate the probability that the professor will need to read a total of more than 1050 pages.
• Why is it so unlikely that the average length of the papers will be less than 12 pages?
• $U\left(\text{10},\text{25}\right)$
• $17.5$
• $\sqrt{\frac{225}{12}}$ = $4.3301$
• $N\left(\text{17.5},\text{0.5839}\right)$
• $N\left(\text{962.5},\text{32.11}\right)$
• $0.0032$

The length of songs in a collector’s CD collection is uniformly distributed from 2 to 3.5 minutes. Suppose we randomly pick 5 CDs from the collection. There is a total of 43 songs on the 5 CDs.

• In words, $X=$
• $X\text{~}$
• In words, $\overline{X}\text{=}$
• $\overline{X}\text{~}$
• Find the first quartile for the average song length.
• The IQR (interquartile range) for the average song length is from _______ to _______.

#### Questions & Answers

how do I set up the problem?
what is a solution set?
Harshika
find the subring of gaussian integers?
Rofiqul
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please can go further on polynomials quadratic
Abdullahi
hi mam
Mark
I need quadratic equation link to Alpa Beta
find the value of 2x=32
divide by 2 on each side of the equal sign to solve for x
corri
X=16
Michael
Want to review on complex number 1.What are complex number 2.How to solve complex number problems.
Beyan
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Mark
use the y -intercept and slope to sketch the graph of the equation y=6x
how do we prove the quadratic formular
Darius
hello, if you have a question about Algebra 2. I may be able to help. I am an Algebra 2 Teacher
thank you help me with how to prove the quadratic equation
Seidu
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Opoku
what is math number
4
Trista
x-2y+3z=-3 2x-y+z=7 -x+3y-z=6
can you teacch how to solve that🙏
Mark
Solve for the first variable in one of the equations, then substitute the result into the other equation. Point For: (6111,4111,−411)(6111,4111,-411) Equation Form: x=6111,y=4111,z=−411x=6111,y=4111,z=-411
Brenna
(61/11,41/11,−4/11)
Brenna
x=61/11 y=41/11 z=−4/11 x=61/11 y=41/11 z=-4/11
Brenna
Need help solving this problem (2/7)^-2
x+2y-z=7
Sidiki
what is the coefficient of -4×
-1
Shedrak
the operation * is x * y =x + y/ 1+(x × y) show if the operation is commutative if x × y is not equal to -1
An investment account was opened with an initial deposit of $9,600 and earns 7.4% interest, compounded continuously. How much will the account be worth after 15 years? Kala Reply lim x to infinity e^1-e^-1/log(1+x) given eccentricity and a point find the equiation Moses Reply A soccer field is a rectangle 130 meters wide and 110 meters long. The coach asks players to run from one corner to the other corner diagonally across. What is that distance, to the nearest tenths place. Kimberly Reply Jeannette has$5 and \$10 bills in her wallet. The number of fives is three more than six times the number of tens. Let t represent the number of tens. Write an expression for the number of fives.
What is the expressiin for seven less than four times the number of nickels
How do i figure this problem out.
how do you translate this in Algebraic Expressions
why surface tension is zero at critical temperature
Shanjida
I think if critical temperature denote high temperature then a liquid stats boils that time the water stats to evaporate so some moles of h2o to up and due to high temp the bonding break they have low density so it can be a reason
s.
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
1 It is estimated that 30% of all drivers have some kind of medical aid in South Africa. What is the probability that in a sample of 10 drivers: 3.1.1 Exactly 4 will have a medical aid. (8) 3.1.2 At least 2 will have a medical aid. (8) 3.1.3 More than 9 will have a medical aid.