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 question posed by the city council. If there are not enough beds 95% of the time, what number of shelter openings (how many more beds) will be needed? Please round to a whole number.

Answer 1

Answer:

397 shelter openings are needed

Explanations:

This is a normal distribution

Mean = 250

Standard Deviation = 75

There are not enough beds 95% of the time

Confidence Level = 95/100 = 0.95

Significance Level (SL) = 1 - Confidence Level (CL)

SL = 1 - 0.95

SL = 0.05

Z-score at 0.05 Significance Level = 1.96

z = 1.96

`\begin{gathered} \text{Mean, }\mu\text{ = 250} \\ \text{Standar Deviation, }\delta\text{ = 75} \end{gathered}`

Let the number of shelter openings be represented by Y

`\begin{gathered} Y\text{ = }\mu\text{ + z}\delta \\ Y\text{ = }250\text{ + 1.96(75)} \\ Y\text{ = 250 + }147 \\ Y\text{ = }397 \end{gathered}`

397 shelter openings will be needed