The histogram below displays the results of a simulated year of births for a Hos
ID: 3204688 • Letter: T
Question
The histogram below displays the results of a simulated year of births for a Hospital that has 50 births per day. The variable is the number of girls born per day. The mean number of girl births per day is 25.060 with a standard deviation of 3.472. (a) Find the number of girl births per day that is one standard deviation below the mean and the number of girl births per day that is one standard deviation above the mean. (b) What proportion of the days in a year have the number of girl births per day been within one standard deviation of the mean? (c) Find the number of girl births per day that corresponds to two standard deviation below the mean and the one that corresponds to two standard deviations above the mean. What proportion of the days in a year have the number of girl births per day been within two standard deviations of the mean? (d) Find the number of girl births per day that correspond to three standard deviations below and above the mean. What proportion of theExplanation / Answer
Answer:
= mean - 1 S.D = 25.060 - 3.472 = 21.588 = ~22 girl births per day.
Number of girl births per day that is 1 standard deviation above the mean
= mean + 1 S.D = 25.060 + 3.472 = 28.532 = ~29 girl births per day.
= mean - 2 S.D = 25.060 – 2*3.472 = 18.116= ~19 girl births per day.
Number of girl births per day that is 2 standard deviation above the mean
= mean + 2 S.D = 25.060 + 2*3.472 = 32.00 = ~32 girl births per day
Proportion of days in a year that have the number of girl births per day within 2 standard deviation of the mean (between 19 and 32 births per day): If we look at the histogram corresponding to these values, there are total 7+15+31+24+25+36+48+38+42+32+23+9+11+7 number of days between 2 standard deviation on either side of the mean = 348days/365 = 0.953 = 95%
= mean - 2 S.D = 25.060 – 3*3.472 = 14.644= ~15 girl births per day.
Number of girl births per day that is 2 standard deviation above the mean
= mean + 2 S.D = 25.060 + 3*3.472 = 35.476 = ~36 girl births per day
Proportion of days in a year that have the number of girl births per day within 3 standard deviation of the mean (between 15 and 36 births per day): If we look at the histogram corresponding to these values, there are total 0+0+3+10+7+15+31+24+25+36+48+38+42+32+23+9+11+7+1+1+0+2 number of days between 3 standard deviation on either side of the mean = 365days/365 = 1 = 100%
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