The mean of X = 10 and the standard deviation of X = 2. The variable X is linearly transformed such that Xnew = a + bX. The mean of Xnew = 800 and the variance of Xnew = 100. Suppose b is a negative number. What does a equal?

The average marks on an Economics Assignment is 55%, with a standard deviation of 5%. The Examiners note that the distribution of the marks is normal. A. Define 'Normal Distribution' including key properties and illustrate with a diagram.  What is the proportion of frequencies below 35%?  What is the proportion of frequencies above 80%?  What is the proportion of marks between 40% and 70% ?

A bakery has determined that the number of loaves of its white bread demanded daily has a normal distribution with mean 7,200 loaves and standard deviation 300 loaves. Based on cost considerations, the company has decided that its best strategy is to produce a sufficient number of loaves so that it will fully supply demand on 94% of all days. a. How many loaves of bread should the company produce? b. Based on the production in part (a), on what percentage of days will the company be left with more than 500 loaves of unsold bread?

There is a normal distribution with mean 10 and standard deviation of 8.  What is the z-score of an observation equaling 15?