Class Exercise 9

Problem 1

Rejean is the drinking water inspector for the city of Lavaland. Historical records show that the arsenic concentration in the drinking water coming from a specific lake is $0.12$ ppm with standard deviation $0.05$ ppm and the distribution is normal. On a recent day, the measurement of the arsenic concentration in drinking water taken from this lake exceeds the safety level of $0.25$ ppm. What is the probability that the arsenic concentration will exceed $0.25$ ppm on a random day? Is this event statistically significant?

Problem 2

The hairy woodpeckers, endemic to North America, have normaly distributed weights (as adults) with mean $\mu = 25\,g$ and standard deviation of $\sigma = 2\,g$. What proportion of hairy woodpeckers:
  1. Have weights exceeding $35\,g$?
  2. Have weights below $21\,g$?
  3. Have weights in the range $21-28\, g$?
What weight corresponds to:
d. The bottom $10\%$ of the distribution?
e. The top $10\%$ of the distribution?

Problem 3

The merlin is a species of small falcons present in Quebec only during the summers. The wingspans of merlins are normally distributed with mean $\mu = 62\,cm$ and standard deviation of $\sigma = 5\,cm$. Compute the values for the $20$th, $40$th, $60$th and $80$th percentile in the distribution of merlin wingspans.