# Standard Normal Probability

Average Precipitation For the first 7 months of the year, the average precipitation in Toledo, Ohio, is 19.32 inches. If the average precipitation is normally distributed with a standard deviation of 2.44 inches find these probabilities.

a. A randomly selected year will have precipitation greater than 18 inches for the first 7 months.

b. Five randomly selected years will have an average precipitation greater than 18 inches for the first 7 months.

https://brainmass.com/statistics/probability/415800

Poisson & Standard Normal Probabilities

1) A survey of citizens over 60 years old who have too much money to qualify for medicaid, but have no health insurance. The ages of the 25 uninsured citizens are:

60 61 62 63 64 65 66 68 68 69 70 73 73

74 75 76 76 81 81 82 86 87 89 90 92

We know that 1/4 of the citizens are below 65.5 years of age.

a. What type of shape does the distribution of the sample appear to have?

b. Calculate the standard deviation of the ages of the uninsured citizens correct to the nearest hundredth of a year.

c. Calculate the coefficient of variation of the ages of the citizens.

2) Suppose Z has a standardized normal distribution with a mean of 0 and a standard deviation of 1. The probability that Z values are larger than______ is 0.6985.

The answer is -0.52. Please show work that supports that answer.

3) Suppose Z has a standardized normal distribution with a mean of 0 and a standard deviation of 1. So, 96% of the possible Z values are between______and________. (symmetrically distributed about the mean)

The answer is -2.05 and 2.05 or -2.06 and 2.06

Please show work to support either of those answers.

4) The number of EMT calls at a hospital has a Poisson distribution with a mean of 6 calls per night.

a. The probability that there will be at least 3 calls in a night is_____.

The answer is 0.9380. Please show work to support that answer.

b. The probability that there will be between 1 and 3 calls per night is_______.

The answer is 0.1487. Please show work to support that answer.