Exercise 4.9 on page 143 was selected.
LA weather, Part II. Exercise 4.7 states that average daily high temperature in June in LA is 77 \(^{◦}\)F with a standard deviation of 5 \(^{◦}\)F, and it can be assumed that they to follow a normal distribution. We use the following equation to convert \(^{◦}\)F (Fahrenheit) to \(^{◦}\)C (Celsius):
\(C=(F−32)×\frac { 5 }{ 9 }\)
- Write the probability model for the distribution of temperature in \(^{◦}\)C in June in LA.
\(N(\mu=25, \sigma=2.78)\)
- What is the probability of observing a 28\(^{◦}\)C (which roughly corresponds to 83 \(^{◦}\)F) temperature or higher in June in LA? Calculate using the \(^{◦}\)C model from part (a).
\(Z = (28-25)/2.78 = 1.08\)
\(1-pnorm(1.08) = 14\%\)
- Did you get the same answer or different answers in part (b) of this question and part (a) of Exercise 4.7? Are you surprised? Explain.
The answer is the same and the slight difference (comparing to 11.5%) is due to the fact that 83 \(^{◦}\)F doesn’t exactly equal 28 \(^{◦}\)C (should be 82.4 \(^{◦}\)F). The 2 units have the same distribution and can be “linearly transformed” to each other.
- Estimate the IQR of the temperatures (in \(^{◦}\)C) in June in LA.
## [1] 3.189805