Question 195376: PLs hELP!!UrGENT!,,nEED youR cOOperAtion..THANK you>>
#1 problem:
A local medical research association proposes to sponsor a footrace. The average time it takes to run the course is 45.8 minutes with a standard deviation of 36 minutes. If the association decides to include only the top 25% of the racers, what should be the cut off time in the tryout run? Assume the variable is normally distributed. Would a person who runs the course in 40 minutes qualify?
#2 problems:
During october, the average temperature Whitman Lake is 53.2 and the standard deviation is 2.3. Assume the variable is normally distributed. For a randomly selected day in october, find the probability that the temperature will be as follows.
a. above 54.
b. below 60.
c. between 49 and 55.
d. if the lake temperature were above 60 would you call it very warm?
#3 problem:
The average time a person spends at the Barefoot Landing Seaquarium 96 minutes. The standard deviation is 17 minutes. Assume the variable is normally distributes. if a visitor is selected at random, find the probability that he or she will spend the following time at the seaquarium.
A. at least 120 minutes
b. At most 80 minutes
c. suggest a time for a bus to return to pick up a group of tourists.
#4 problem:
The average commute to work(one way) is 25.5 minutes according to the 2000 census. If we assume that commuting times are normally distributed with a standard deviation of 6.1 minutes, what is the probability that a randomly selected commuter spends more than 30 minutes a day commuting one way?
#5 problem:
If the average price of a new home is $145,500, find the maximum and minimum prices of the houses that a contractor will build to include the middle 80% of the market. Assume that the standard deviation of prices $1500 and the variable is normally distributed
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! #1 problem:
A local medical research association proposes to sponsor a footrace. The average time it takes to run the course is 45.8 minutes with a standard deviation of 36 minutes.
If the association decides to include only the top 25% of the racers, what should be the cut off time in the tryout run?
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The z that corresponds to the top 25% is 0.6745
Then x = z*s + u
x = 0.6745*36 + 45.8 = 70.08 minutes (cut-off time)
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Assume the variable is normally distributed.
Would a person who runs the course in 40 minutes qualify?
Ans: Absolutely
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#2 problems:
During october, the average temperature Whitman Lake is 53.2 and the standard deviation is 2.3.
Assume the variable is normally distributed. For a randomly selected day in october, find the probability that the temperature will be as follows.
a. above 54.
b. below 60.
c. between 49 and 55.
d. if the lake temperature were above 60 would you call it very warm?
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Find the z value of each of these using z = (x-u)/s
Then find the answer to the question.
Example
a. above 54
z(54) = (54-53.2)/2.3 = 0.3478
P(temperature is above 54) = P(z > 0.3478) = 0.3640
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#3 problem:
The average time a person spends at the Barefoot Landing Seaquarium 96 minutes. The standard deviation is 17 minutes. Assume the variable is normally distributes. if a visitor is selected at random, find the probability that he or she will spend the following time at the seaquarium.
A. at least 120 minutes
b. At most 80 minutes
c. suggest a time for a bus to return to pick up a group of tourists.
Comment: Use the same procedure as in question #2
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#4 problem:
The average commute to work(one way) is 25.5 minutes according to the 2000 census. If we assume that commuting times are normally distributed with a standard deviation of 6.1 minutes, what is the probability that a randomly selected commuter spends more than 30 minutes a day commuting one way?
#5 problem:
If the average price of a new home is $145,500, find the maximum and minimum prices of the houses that a contractor will build to include the middle 80% of the market. Assume that the standard deviation of prices $1500 and the variable is normally
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Comment:
#4 and #5 are worked the same as 1-3. Find the appropriate z score. Then
convert to an x score using x = zs + u
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Cheers,
Stan H.
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