You are asked to do a study of shelters for abused and battered women to determi

Question

You are asked to do a study of shelters for abused and battered women to determine the necessary capacity in your city to provide housing for most of these women. After recording data for a whole year, you find that the mean number of women in shelters each night is 250, with a standard deviation of 75. Fortunately, the distribution of the number of women in the shelters each night is normal, so you can answer the following questions posed by the city council.

If the city’s shelters have a capacity of 350, will that be enough places for abused women on 95% of all nights? If not, what number of shelter openings will be needed?

The current capacity is only 220 openings, because some shelters have been closed. What is the percentage of nights that the number of abused women seeking shelter will exceed current capacity?

Explanation / Answer

Solution:-

= 250, = 75

a) 397 would be the enough places for abused women on 95% of all nights.

95% confidence interval for abused and battered women is C.I = (103, 397).

C.I = xbar + zalpha/2 × S.E

C.I = 250 + 1.96 × 75

C.I = 250 + 147

C.I = (103, 397)

397 would be the enough places for abused women on 95% of all nights.

b) The percentage of nights that the number of abused women seeking shelter will exceed current capacity is 65.54%.

By applying normal distribution:-

z = (x - )/

z = - 0.4

P(z > - 0.4) = 0.6554

P(z > - 0.4) = 65.54%

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