SOLUTION: A city in the USA is trying to increase tourism. The tourism division would like to include in its tourism brochure the middle range of temperatures that occur on 90% of the days

Question 40009: A city in the USA is trying to increase tourism. The tourism division would like to include in its tourism brochure the middle range of temperatures that occur on 90% of the days there. A check with the Weather Service finds that the average temperature in this city is 76 degrees with a standard deviation of 5.7 (the temperatures were normally distributed). Find the two temperatures that cut off the middle 90% of temperatures in this city.
I don't know the source of this problem. I'm trying to get some help for a friend who is trying to understand these type of problems. Thank you for your assistance.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A city in the USA is trying to increase tourism. The tourism division would like to include in its tourism brochure the middle range of temperatures that occur on 90% of the days there. A check with the Weather Service finds that the average temperature in this city is 76 degrees with a standard deviation of 5.7 (the temperatures were normally distributed). Find the two temperatures that cut off the middle 90% of temperatures in this city.
Sketch a normal curve. Put mean at center = 76 and note that standard dev.
is 5.7
Sketch a standard normal curve with center at 0 and std. dev. of "1".
Use your z-chart to determine the z-values that bracket 90% of the area
under the standard normal curve. Those values are -1.65 and +1.65.
Now find the termperatures on your 1st curve that correspond to those
z-values using the formuls z(x)=[x-mu]/sigma where z=1.65 or -1.65, mu=76 and
sigma=5.7.
1.65=[x-76]/5.7
x=(5.7)(1.65)+76
x=85.405
Also x=(5.7)(-1.65)+76
x=66.595
So the range of termperatures between 66.505 and 85.4-5 contain 90% of the
termperatures for that city.
Cheers,
Stan H.

RELATED QUESTIONS
In one town, 37% of adults are employed in the tourism industry. What is the probability... (answered by lynnlo)

In one town, 35% of adults are employed in the tourism industry. What is the probability... (answered by mathsolverplus,greenestamps,ikleyn)

The approximate number of tourists in South America is 40.3million and its average rate... (answered by Rongtian)

The Tennessee Tourism Institute (TTI) plans to sample information center visitors... (answered by stanbon)

The Tennessee Tourism Institute (TTI) plans to sample information center visitors... (answered by Boreal)

The states of Hawaii and Pennsylvania spend a total of $60.9 million for tourism. The... (answered by checkley75)

The States C and D spend a total of $55.4 million for tourism. The state C spends $2.4... (answered by ewatrrr)

the states c and d spend a total of $55.6 million dollars for tourism, the state c spends (answered by solver91311)

The Manitoba Tourism Board plans to sample information centre visitors entering the... (answered by Theo)