SOLUTION: plS help me!.. URgent..I need your cooperatioN! #1 problem: The Old Farmer's Almanac reports that the average person uses 123 gallons of water daily. If the standard deviatio

Question 195602: plS help me!.. URgent..I need your cooperatioN!

#1 problem:
The Old Farmer's Almanac reports that the average person uses 123 gallons of water daily. If the standard deviation is 21 gallons, find the probability that the mean of a randomly selected sample of 15 people will be between 120 and 126 gallons. Assume the variable is normally distributed.
#2 problem:
Procter & Gamble reported that an American family of four washes an average of 1 ton (2000 pounds) of clothes each year. If the standard deviation of the distribution is 187.5 pounds, find the probability that the mean of a randomly selected sample of 50 families of four will be between 1980 and 1990 pounds.

#3 problem:
The average time it takes a group of adults to complete a certain achievement test is 46.2 minutes. The standard deviation is 8 minutes. Assume the variable is normally distributed.
a.) Find the probability that a randomly selected adult will complete the test in less than 43 minutes.
b.) Find the probability that, if 50 randomly selected adult take the test, the mean time it takes the group to complete the test will be less than 43 minutes.
c.)Does it seem reasonable that an adult would finish the test in less than 43 minutes? Explain.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
#1 problem:
The Old Farmer's Almanac reports that the average person uses 123 gallons of water daily. If the standard deviation is 21 gallons, find the probability that the mean of a randomly selected sample of 15 people will be between 120 and 126 gallons. Assume the variable is normally distributed.
#2 problem:
Procter & Gamble reported that an American family of four washes an average of 1 ton (2000 pounds) of clothes each year. If the standard deviation of the distribution is 187.5 pounds, find the probability that the mean of a randomly selected sample of 50 families of four will be between 1980 and 1990 pounds.
---------------
Find the z-values of 1980 and 1990
z(1980) = (1980-2000)/[187.5/sqrt(50)] = -0.7542
z(1990) = (1990-2000)/[187.5/sqrt(50)] = -0.37712
-----------
The P(1980 < xbar < 1990) = P(-0.7542 < z < -0.3771) = 0.1277
=====================================================================
#3 problem:
The average time it takes a group of adults to complete a certain achievement test is 46.2 minutes. The standard deviation is 8 minutes. Assume the variable is normally distributed.
a.) Find the probability that a randomly selected adult will complete the test in less than 43 minutes.
---
z(43) = (43-46.2)/8 = -0.4
---
P(x < 43) = P(z < -0.4) = 0.3446
=========================================================================

b.) Find the probability that, if 50 randomly selected adults take the test, the mean time it takes the group to complete the test will be less than 43 minutes.
---
z(43) = (43-46.2)/[8/sqrt(50)] = -2.8284
---
P(xbar < 43) = P(z < -2.8284) = 0.0023
==========================================================================

c.)Does it seem reasonable that an adult would finish the test in less than 43 minutes? Explain.
He has better than a 34% chance of doing that, as seen above.
Cheers,
Stan H.

RELATED QUESTIONS
An almanac reports that the average person uses 118 gallons of water daily. If the... (answered by penguin_129)

PLs hELP!!UrGENT!,,nEED youR cOOperAtion..THANK you>> #1 problem: A local medical... (answered by stanbon)

pls i need urgent help here. Find the accumulated value of an investment of $9000 at 9%... (answered by checkley77)

Thanks for the previous questions answered. Pls, I need your help here, and it is urgent (answered by solver91311,Earlsdon)

Please help me solve this problem. The average American uses 100 gallons of water each... (answered by scott8148)

pls help me with this math; it's that urgent Find a polynomial function with the given (answered by stanbon)

need help! urgent!pls. For a freely-falling object dropped from rest, what is its... (answered by Edwin McCravy)

Help, I am trying to help my daughter with her homework, don't know what I'm doing. Hope (answered by stanbon)

thanks for the previous answer. Pls, I need help in this one. it's that urgent Factor... (answered by Earlsdon)