Question

1. Assume that your data comes from a Normal distribution. Further assume that the distribution has pop-ulation mean μ equal to your sample mean ̄x and population standard deviationσequal to your samplestandard deviations. Draw the graph of the Normal distribution described, labeling the mean and the tickmarks at standard deviation units.

2. We were sampling from the distribution of rainfall in a particular month. Assuming this distribution is Normal, find the proportion of years in which rainfall in the selected month exceeds 3 inches.

The number are: 1, 1.05, 1.29, 1.33, 1.67, 1.75, 2.64, 2.84, 3.69, 3.96, 4.55, 4.63, 4.81, 4.82, 5.12, 5.37, 5.47, 5.62, 5.66, 5.94, 6.2, 6.46, 6.97, 7.3, 7.36, 9.5, 10.25, 10.29, 12.75, 12.82

Answer 1

1. The normal curve

2. For the given 30 samples the mean is calculated as

And using excel as

Mean=5.437

Similarly the standard deviation is calculated using excel tool as

Hence to find the proportion who is above 3 inches we need to use Z formula as

Now the proportion above the Z=-0.75 is computed using Z table shown below as 0.7734