Since January Pohnpei has been experiencing sunnier, drier than normal weather due to a mild El Niño event. Pohnpei is naturally a rainy place. The rains of summer seem to be returning to the island during this past week. With that in mind the test tackles some rainy day statistics. The average number of days with rain per month is 21.7 days with a standard deviation of 2.7 days. The distribution of the number of days with rain per month is normally distributed.

- _______ What is the probability a month will have more than 21.7 days of rain?
- _______ What is the probability a month will have less than 19 days of rain?
- _______ What is the probability a month will have more than 23 days of rain?
- _______ What is the probability a month will have between 19 and 23 days of rain?
- _______ How many days of rain in the rainiest 20% of the months?
- _______ What is the probability that four months will average less than 19 days of rain?
- Presume that the average of 21.7 rainy days per month with a standard deviation of 2.7 rainy days per month is based on a sample study of thirty-six months. Use this data to calculate a c = 90% confidence interval for the population mean µ.
- Use the information above to sketch the 90% confidence interval and other information to set up this problem:

- _______ Determine the area in the left tail.
- _______ Determine the area in the right tail.
- _______ Determine the left z value.
- _______ Determine the right z value.
- _______ Determine the left (lower) bound for the population mean µ.
- _______ Determine the right (upper) bound for the population mean µ.
- The confidence interval for the population mean µ is:

P( _________ < µ < _________ ) = _________

Statistic or Parameter Symbol Equations Excel Normal Statistics 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 Calculate a z-statistic from an **x**z =( **x**- µ)/(sx/SQRT(n))Calculate a t-statistic (t-stat) t =( **x**- µ)/(sx/SQRT(n))Calculate an **x**from a z=µ + z _{c}*sx/sqrt(n)Find a probability p from a z value =NORMSDIST(z) Find a z value from a probability p =NORMSINV(p) Confidence interval statistics Degrees of freedom df = n-1 =COUNT(data)-1 Find a z _{c}value from a confidence level cz _{c}=ABS(NORMSINV((1-c)/2)) Find a t _{c}value from a confidence level ct _{c}=TINV(1-c,df) Calculate an error tolerance E of a mean for n >= 30 using sx E =z _{c}*sx/SQRT(n)Calculate an error tolerance E of a mean for n < 30 using sx. Can also be used for n >= 30. E =t _{c}*sx/SQRT(n)Calculate a confidence interval for a population mean µ from a sample mean **x**and an error tolerance E**x**-E<= µ <=**x**+E - Use the information above to sketch the 90% confidence interval and other information to set up this problem: