The first step in this problem is calculating the z-score. 

The next step is to look up 4 in the z-table. The value from the table is .

A -score indicates whether a particular value is typical for a population or data set.  The closer the -score is to 0, the closer the value is to the mean of the population and the more typical it is.  The -score is calculated by subtracting the mean of a population from the particular value in question, then dividing the result by the population's standard deviation. 

A Z-score indicates whether a particular value is typical for a population or data set.  The closer the Z-score is to 0, the closer the value is to the mean of the population and the more typical it is.  The Z-score is calculated by subtracting the mean of a population from the particular value in question, then dividing the result by the population's standard deviation.

To find the z-score, follow the formula

or

A z score is unique to each value within a population.

To find a z score, subtract the mean of a population from the particular value in question, then divide the result by the population's standard deviation.

We need to calculate Natalie's z-scores for both her Spanish and math exams. Calculating z-scores is as follows:

Her z-score for the Spanish exam is , which equals 1.25, while her z-score for the math exam is , which equals 1.50. Since both z-scores are positive, Natalie did above average on both tests, but since her z-score for the math exam is higher than her z-score for the Spanish exam, Natalie did better on her math exam when compared to the rest of her peers taking the exam.

To find the z-score, we follow the formula

 where  is the given value,  is the mean, and  is the standard deviation.

For this problem we see that

    and 

Substituting for these values we see

 is the average life of the bread maker, in this problem 9 years.

 is the standard deviation of the break makers life. The standard deviation is the square root of the variance. 

X is the test statistic we are looking to find. In this problem it is the probability that the bread maker lasts less than 13 years.

If you were to find the value associated with a z-score of 2 on the z-table, you would see that

A t test is used to compare the means of different groups.  A t test score describes the likelihood that the difference in means between two groups is due to chance. The null hypothesis assumes the two sets are equal however, one can reject the null hypothesis with a p value within a particular confidence level.

Use the fact that the sum of  squared standard and independent normal variables follows a chi-squared distribution with degrees of freedom.