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In a particular faculty 60% of students are men and 40% are women. In a random sample of 50 students what is the probability that more than half are women?
Let the random variable X = number of women in the sample.
Assume X has the binomial distribution with n = 50 and p = 0.4.
a. What is the expected value and variance of the random variable X?
b. Calculate the exact binomial probability.
c. Are the conditions that permit you to use a normal approximation to the binomial satisfied? Explain
d. Recalculate the probability in part b using a normal approximation without the continuity correction.
e. Recalculate the probability in part b using a normal approximation with the continuity correction.
Batch has just been completed. Determine probability that first three units manufactured in this batch will contain at least total of 4 defects?
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The network is said to be robust if at least one of the three servers operate more than 2 years. What is the probability that the network is robust?
How large a sample must one take to be 90% confident that the estimate is within 0.05 of the true proportion and find the 99% confidence interval of the population proportion of persons living in Phoenix who are obese.
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What sample size is needed to estimate the proportion of Americans who favor tougher gun control with 95% confidence and maximum error of 3%. Assume past studies indicted that the proportion is around 40%.
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