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vredina [299]
3 years ago
13

San Francisco is one of the most expensive cities in which to live in the United States. As of February 2013, the mean rent for

a one-bedroom apartment in the Mission District was $2600.6 Assume that the distribution of rents is approximately normal and the standard deviation is $200. A one-bedroom apartment in the Mission District is selected at random. (a) Find the probability (±0.0001) that the rent is less than $2470. P(X<2470) =
(b) Find the probability (±0.0001)that the rent is between $2560 and $2640. P(2560⩽X⩽2640) =

(c) Find a rent r (±0.01) such that 90% of all rents are less than r dollars per month. r =

Mathematics
1 answer:
kramer3 years ago
6 0

Answer:

a) 0.2569 or 25.69%

b) 0.1585 or 15.85%

c) $2,856.91

Step-by-step explanation:

a)  

Here we want to calculate the area between 0 and 2,470 (since no rent is negative) under the Normal curve of mean 2,600.6 and standard deviation 200.

We can do this easily with a spreadsheet and we get that the probability is <em>0.2569 or 25.69%</em> (See picture 1)

b)

Now we look for the area under the curve between 2,560 and 2,640 which is <em>0.1585 or 15.85%</em> (See picture 2)

c)

Here we are looking for a value r such that the area under the curve to the left of r is 90%=0.9.

Again, using the computer we find that value is <em>r= $2,856.91 </em>

(See picture 3)

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