- A survey was administered to 193 people this past summer in Chuuk on the length of time it takes to commute to the Chuuk state campus. The results of this survey are in the table below. Times ranged from a few minutes to an hour and fifteen minutes. The following data is divided into 15 minute time spans.

Time in minutes Number of people Rel. Freq. P ( x ) x * P ( x ) 15 63 30 28 45 35 60 30 75 37 **Sums:**- Calculate the relative frequency P(x) values for the third column.
- Use the fourth column, x*P(x), to calculate the mean length of time for people to commute to the Chuuk campus.

The diagram above depicts three normal curves

- _______ Which curve has the largest mean?
- _______ Which curve has the largest standard deviation?
- _______ What is the mean for curve A?
- _______ What is the mean for curve B?
- _______ What is the mean for curve C?
- _______ What is the standard deviation for curve C?

- Sapporo Draft beer in a bottle is produced in batches with a mean alcohol content of 5.5. There is a standard deviation of 0.5. Presume that the distribution of alcohol content is normal.
- What is the probability a batch of Sapporo Draft beer will have an alcohol content of less than 5?
- What is the probability a batch of Sapporo Draft beer will have an alcohol content of between 5.5 and 6.2?
- Suppose, as part of a quality control program, Sapporo plans to not sell the 10% of the batches with the lowest alcohol content. What alcohol content is the value below which a batch will not be sold? Nota bene (hint): This is an inverse problem. The area is the 10% in the left tail.

Statistic or Parameter | Symbol | Equations | Excel |
---|---|---|---|

Calculate a z value from an x | z | ^{= } |
=STANDARDIZE(x, µ, s) |

Calculate an x value from a z | x | = s z + µ | = s*z+µ |

Find a probability p from a z value | =NORMSDIST(z) | ||

Find a z value from a probability p | =NORMSINV(p) |