A random sample of size 16 is taken from the normal distribu

A random sample of size 16 is taken from the normal distribution with mean 20 and variance 4. Let X bar denote the sample average. What is the probability that X bar is larger than 19? Professor A says he deserves a raise because his students have an exceptionally high success rate on the engineering certification exam. The dean compared the success rates of 40 randomly selected students from Professor A\'s classes and 40 randomly selected students from his own classes. Twenty four of Professor A\'s group passed the exam and 19 of the students from the dean\'s classes passed. Find a 95% confidence interval for the difference between the success rates of Professor A and the dean. It is known that about 20% of all income tax returns have errors. Government officials would like to know that percentage more precisely, to two significant digits. They intend to survey a sample of tax returns. How large a sample should they take to achieve the desired accuracy with 90% confidence? An astronomer collects data on the distance from Earth and the velocity of recession of several dozen galaxies. Which of the following statements is not true? Ten pairs of chicks were selected to test the effect of a vitamin supplement on early

Solution

5.

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    19      
u = mean =    20      
n = sample size =    16      
s = standard deviation =    2      
          
Thus,          
          
z = (x - u) * sqrt(n) / s =    -2      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   -2   ) =    0.977249868 [ANSWER]

*******************************************

Hi! Please submit the next part as a separate question. That way we can continue helping you! Please indicate which parts are not yet solved when you submit. Thanks!