Length of Pregnancy Assume that the lengths of pregnancy for humans is approximately Normally distributed , with a mean of 267 days and a standard deviation of 10 days. Use the Empirical Rule to answer the following questions. Do not use the technology or the Normal table. Begin by labeling the horizontal axis of the graph with lengths, using the given mean and standard deviation. Three of the entries are done for you. a. Roughly what percentage of pregnancies last more than 267 days? i. almost all ii. 95% iii. 68% iv. 50% b. Roughly what percentage of pregnancies last between 267 and 277 days? i. 34% ii. 17% iii. 2.5% iv. 50% c. Roughly what percentage of pregnancies last less than 237 days? i. almost all ii. 50% iii. 34% iv. about 0% d. Roughly what percentage of pregnancies last between 247 and 287 days? i. almost all ii. 95% iii. 68% iv. 50% e. Roughly what percentage of pregnancies last longer than 287 days? i. 34% ii. 17% iii. 2.5% iv. 50% f. Roughly what percentage of pregnancies last longer than 297 days? i. almost all ii. 50% iii. 34% iv. about 0%
Length of Pregnancy Assume that the lengths of pregnancy for humans is approximately Normally distributed , with a mean of 267 days and a standard deviation of 10 days. Use the Empirical Rule to answer the following questions. Do not use the technology or the Normal table. Begin by labeling the horizontal axis of the graph with lengths, using the given mean and standard deviation. Three of the entries are done for you. a. Roughly what percentage of pregnancies last more than 267 days? i. almost all ii. 95% iii. 68% iv. 50% b. Roughly what percentage of pregnancies last between 267 and 277 days? i. 34% ii. 17% iii. 2.5% iv. 50% c. Roughly what percentage of pregnancies last less than 237 days? i. almost all ii. 50% iii. 34% iv. about 0% d. Roughly what percentage of pregnancies last between 247 and 287 days? i. almost all ii. 95% iii. 68% iv. 50% e. Roughly what percentage of pregnancies last longer than 287 days? i. 34% ii. 17% iii. 2.5% iv. 50% f. Roughly what percentage of pregnancies last longer than 297 days? i. almost all ii. 50% iii. 34% iv. about 0%
Solution Summary: The given graph represents the density curve for the length of the pregnancy for humans with the mean of 267 days, and standard deviation of 10 days.
Length of Pregnancy Assume that the lengths of pregnancy for humans is approximately Normally distributed, with a mean of 267 days and a standard deviation of 10 days. Use the Empirical Rule to answer the following questions. Do not use the technology or the Normal table. Begin by labeling the horizontal axis of the graph with lengths, using the given mean and standard deviation. Three of the entries are done for you.
a. Roughly what percentage of pregnancies last more than 267 days?
i. almost all
ii. 95%
iii. 68%
iv. 50%
b. Roughly what percentage of pregnancies last between 267 and 277 days?
i. 34%
ii. 17%
iii. 2.5%
iv. 50%
c. Roughly what percentage of pregnancies last less than 237 days?
i. almost all
ii. 50%
iii. 34%
iv. about 0%
d. Roughly what percentage of pregnancies last between 247 and 287 days?
i. almost all
ii. 95%
iii. 68%
iv. 50%
e. Roughly what percentage of pregnancies last longer than 287 days?
i. 34%
ii. 17%
iii. 2.5%
iv. 50%
f. Roughly what percentage of pregnancies last longer than 297 days?
i. almost all
ii. 50%
iii. 34%
iv. about 0%
Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.
6. Show that
1{AU B} = max{1{A}, I{B}} = I{A} + I{B} - I{A} I{B};
I{AB} = min{I{A}, I{B}} = I{A} I{B};
I{A A B} = I{A} + I{B}-21{A} I {B} = (I{A} - I{B})².
Theorem 3.5 Suppose that P and Q are probability measures defined on the same
probability space (2, F), and that F is generated by a л-system A. If P(A) = Q(A)
for all A = A, then P = Q, i.e., P(A) = Q(A) for all A = F.
6. Show that, for any random variable, X, and a > 0,
Lo P(x
-00
P(x < x
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