1) The length of human pregnancies from conception to birth varies according to a distribution that is approximately normal with mean 266 days and standard deviation 16 days.
a) Find the probability a randomly selected pregnancy lasts less than 240 days. (Show your work.)
From the normal distribution table the value equivalent to 95% confidence interval is 1.96. Therefore confidence interval for pregnancy
266+ or 1.96 (16240)
266.130667 U 265.86933
b) Shade in the area in the curve below representing the probability you found in part a) in terms of X, the length of pregnancy. Be sure to label the probability, the mean, and x0, and the numbers for each of these 3 items.
Z1 z0 z2
Z0= 240 days
c) What percent of pregnancies last between 240 and 270 days (roughly between 8 months and 9 months)? (Show your work.)
Percentage of pregnancies that last between 240 and 270day
d) How long do the longest 20% of pregnancies last? (Show your work.)
2) The data set airquality.xlsx contains the daily readings of the following air quality values in New York for May 1, 1973 to September 30, 1973.
Ozone: Mean ozone in parts per billion (ppb) from 1pm to 3pm at Roosevelt Island
SolarR: Solar radiation in langleys in the frequency band 4000-7700 Angstroms from 8am to 12pm at Central Park
Wind: Average wind speed in miles per hour at 7am and 10am at LaGuardia Airport
Temp: Maximum daily temperature in degrees Fahrenheit at LaGuardia Airport
Two additional variables include Month and Day on which the measurements were taken.
a) Create a Normal quantile (Q-Q) plot of the variable Wind. Does this variable appears to be Normally distributed? Why or why not? Circle any problematic areas on the plot.
This variable appears to be normal distribution because it seems 50% of the variables are more than mean and the other 50% of the variables seems to be less than the mean. It is also likely to note that in normal distribution mean, mode and median are equal to each other and in this case, they are close to each other. This is a significant sign that these variables are normally distributed.
b) Create a histogram of the variable Wind. Describe the shape of this histogram and how this description matches what you say on the Normal quantile plot.
This histogram is bell shaped. This indicates that the variables are normally distributed as 50% of the variables appear on one side and the rest 50% on the other side.
a) Create a Normal quantile (Q-Q) plot of the variable Ozone. Does this variable appear to be normally distributed? Why or why not? Circle any problematic areas on the plot.
These variables about Ozone do not appear to be normally distributed. This is because most of the variables are not appear one side indicating that 50% of these variables are not equal or less than the mean. They therefore appear on one side hence does not form bell shaped as normal distribution appear.
b) Create a histogram of the variable Ozone. Describe the shape of this histogram and how this description matches what you say on the Normal quantile plot.
This histogram has skewed distribution because most of the variables appear more than the average on one side of it. The peak of the distribution is not centrally placed and therefore its tails stretches away.
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