(d) In a group of three professors selected at random, what is the expected number of extroverts? (e)What is the standard deviation of the distribution? (Round your answer to two decimal places.) (f) Suppose you were assigned to write an article for the student newspaper and you were given a quota (by the editor) of interviewing at least three extroverted professors. How many professors selected at random would you need to interview to be at least 89% sure of filling the quota? (Enter the smallest number of professors needed.)

Let x be a random variable representing the starting salary of a first-year teacher in a city.  A report claims that the mean starting salary of these first-year teachers is less than $52,000.  To test this claim we find that a random sample of 25 teachers has a mean starting salary of $51,875 with a sample standard deviation of $1,055.  If you assume that the population mean is $52,000, find the P-value corresponding to the hypothesis that the mean starting salary of the first-year teachers is less than $52,000.   A. 0.28   B. 0.56   C. 0.14   D. 0.36

A gambler complained about the dice. They seemed to be loaded! The dice were taken off the table and tested one at a time. One die was rolled 300 times and the following frequencies were recorded. Outcome 1 2 3 4 5 6 Observed frequency O 63 45 60 33 49 50 Do these data indicate that the die is unbalanced? Use a 1% level of significance. Hint: If the die is balanced, all outcomes should have the same expected frequency. (a) What is the level of significance?   (b) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to at least three decimal places. Round the test statistic to three decimal places.)   What are the degrees of freedom?

A Statistics class has 85 students. 48 of these are females and 37 are males. A random sample of 11 students in the class is selected. Let X = the number of the selected students who are female. a. What is the expected value of X? b. What is the standard deviation of X? c. What is the probability that X is within 2.0 standard deviations of its expected value? d. What is the probability that X = 1.5?

A psycho-linguist has been studying the frequency of text-speech (e.g., R U Ok?, LOL ) has been progressing into EMAIL correspondence.  He collects a sample of 121 EMAIL messages and computes the mean (average) number of examples of text-speech per message.  He also has a huge library of archived EMAIL messages from the year 2001.  From these he is able to calculate the population average and standard deviation.  Compute a inferential statistic to evaluate the hypothesis that the use of text-speech has increased in the years since 2001.  Use an alpha level that would insure a maximum of a %5 risk of rejecting a true null hypothesis.  These are the obtained values: Population Mean from 2001:                          1.6       Population Standard deviation from 2001:    1.25     Sample mean from this year:                           1.98        The appropriate statistics to use is a ___ test.

. The on-campus housing costs for a semester at a state university are Normally distributed with a mean of $1553 and a standard deviation of $329.(a) What is the distribution of the mean on-campus housing cost for a semester at this university for a random sample of 50 students? (b) What is the probability that a randomly selected on-campus student spends more than $1200 per semester? (c) What is the probability that a random sample of 50 students spends an average of less than $1500? (d) What is the probability that a random sample of 50 students spends an average of $1450 to $1600 per semester?

Suppose that a recent poll found that 41% of adults believe that the overall state of moral values is poor. Complete parts (a) through (c). (a) For 250 randomly selected adults, compute the mean and standard deviation of the random variable X, the number of adults who believe that the overall state of moral values is poor. The mean of X is. (Round to the nearest whole number as needed.)

A hospital wants to determine if the type of treatment for pneumonia is a factor in recovery time? The table below shows the number of days to recovery for several randomly selected pneumonia patients that had various types of treatment. A Few Hours in the Hospital Overnight Hospital Stay Sent Home With Medicine 10 8 27 15 12 21 12 17 24 13 10 28 11 12 20 11 12 22 10 18 14 16   12 16     Assume that all distributions are normal, the three population standard deviations are all the same, and the data was collected independently and randomly. Use a level of significance of α=0.05α=0.05.H0: μ1=μ2=μ3H0: μ1=μ2=μ3Ha:Ha: At least two of the means differ from each other. For this study, we should use              The test-statistic for this data =  (Please show your answer to 4 decimal places.) The p-value for this sample =  (Please show your answer to 4 decimal places.)

Waiting time for service at a Bank has a mean of 65 seconds and a standard deviation of 25 seconds. The Bank manager assures that the probability of waiting should not exceed 99.3% for 1.6 standard deviations from the average wait time. If a customer waits 1.6 standard deviations exceeding the average wait time, what is the expected wait time for this customer in seconds (Assume wait time is normally distributed)? O a. 123.16 O b. 25.00 O c. 125.22 O d. 105.00 O e. 126.43 Of. 124.14