Statistics and Probabillity questions (Help)
Can someone please help me with any of these questions? Can you solve any of these and show me how you got to the answer? This is my school midterm review but I don;t know how to doit... Thanks~
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 1. Data collected over a long period of time show that a particular genetic defect
occurs in 1 of every 1000 children. The records of a medical clinic show X = 60 children
with the defect in a random sample of 50,000 examined. What is the probability of ob-
serving a value of X equal to 60 or more? Would you say that the observation of X = 60
children with genetic defect was rather unlikely?
2. Suppose a random sample of n = 25 observations is selected from a population
that has normal distribution with mean 106 and standard deviation 12.
 a. Give the mean and standard deviation of the sample mean ¯X .
 b. Find the probability that ¯X exceeds 110.
 c. Find the probability that the sample mean deviates from the population mean by
no more than 4.
3. Yearly income for a certain category of workers with 4 years of experience in a certain
Canadian province is believed to average $70,540 with a standard deviation of $4,000. In
an attempt to verify this assumption, a random sample of 36 workers of that category
 a. Describe the sampling distribution of the sample mean ¯X .
 b. Within what limits would you expect the sample average to lie, with probability
 c. Calculate the probability that the sample mean ¯X is smaller than $68, 500.
 d. If your random sample actually produced a sample mean of $68, 500, would you
consider this rather unusual? What conclusion might you draw?
 4. In a report of why e-shoppers abandon their online sales transaction, a study
found that “pages took too much time to load” and “site was too confusing so that I
couldn’t find the product” were the two complaints heard most often. Based on 50 cus-
tomers’ responses, the average time to complete online order form will take 4.5 minutes
and that the standard deviation of the time to complete an online order is 2.7 minutes.
Construct a 95% confidence interval for μ the average completion time for an online order.
 5. In a pool of n = 800 randomly selected adults, 360 indicated that movies were
getting better. Construct a 99% confidence interval for the overall proportion of adults
who say that movies are getting better.
6. Suppose the number of successes in n = 300 binomial trials is 27.
 a. Find a 90% confidence interval for p, the probability of success at each trial.
 b. Same question with a level of confidence 98%. Why is this interval wider than the