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A doctor is called to see a sick child. The doctor has prior information that 90% of sick children in that neighborhood have the flu, while the other 10% are sick with measles.   A well-known symptom of measles is a rash.  Assume that the probability of having a rash if one has measles is 95%. However, occasionally children with flu also develop rash, and the probability of having a rash if one has flu is 8%.   Upon examining the child, the doctor finds a rash. What is the probability that the child has measles?

A synthetic fiber has tensile strength is distributed with mean 76 psi and and standard deviation 4 psi. What is the probability that a random sample of eight specimens will have tensile strength that exceeds 78 psi?

Resistors manufactured by a certain company have a mean resistance of 100 ohms and a variance of 64 ohms. What is the probability that the average resistance of a sample of 36 resistors will be between 97 and 102 ohms?

An independent research was made to calculate the mean weight of elder people in Russia. 50 men and women were interviewed for this research. Calculate the sample median, mode, and mean of the data. Explain how these three measures of location describe different features of the data. All values are in kg. (You will use this data set to answer several questions, Once you entered into calculator Do not delete it).   Calculate the Sample Variance.

A sociologist focusing on popular culture and media believes that the average number of hours per week (hrs/week) spent using social media is greater for women than for men. Examining two independent simple random samples of 100 individuals each, the researcher calculates sample standard deviations of 2.3 hrs/week and 2.5 hrs/week for women and men respectively. If the average number of hrs/week spent using social media for the sample of women is 1 hour greater than that for the sample of men, what conclusion can be made from a hypothesis test ?

Suppose that a lifetime of a component (in hours) , X, is modeled with a Weibull distribution with  and . Determine . (i.e. Given that the system has lasted more than 3000 hours, what is the probability it will last for more than 6000 hours?)

Web crawlers need to estimate the frequency of changes to Web sites to maintain a current index for Web searches. Assume that the changes to a Web site follow a Poisson process with a mean of 6 days. Let a random variable X denote the time (in days) until the next change.   What is the probability that the next change occurs in less than 4.5 days?

A company claims that 9 out of 10 doctors recommend its brand of cough syrup to their patients. To test this claim against the alternative that the actual proportion is less than 90%, a random sample of 100 doctors was chosen which resulted in 97 who indicate that they recommend this cough syrup. Find the P-value for this test.

West Virginia State Board of Education v. Barnette (1943) was significant because it

Which of the following statements regarding the Supreme Court overturning acts of Congress is correct?