# 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.

#### Solution Summary

The solution provides step by step method for the calculation of Poisson and standard normal probabilities. Formula for the calculation and Interpretations of the results are also included.