LA weather

The average daily high temperature in June in LA is $\({{params.mu}} ^{\circ} F\)\( with a standard deviation of \)\({{params.sig}} ^{\circ} F\)\(, and it can be assumed that they do follow a normal distribution. We use the following equation to convert \)\(^{\circ} F\)\( (Fahrenheit) to \)\(^{\circ} C\)$ (Celsius):

\[C = (F-32)\cdot \frac{5}{9}\]

Part 1

Write the mean of the probability model for the distribution of temperature in $\(^{\circ} C\)$ in June in LA.

Part 2

Write the standard deviation of the probability model for the distribution of temperature in $\(^{\circ} C\)$ in June in LA.

Part 3

What is the probability of observing a $\({{params.temp_C}} ^{\circ} C\)\( (which roughly corresponds to \)\({{params.temp}} ^{\circ} F\)\() temperature or higher in June in LA? Calculate using the \)\(^{\circ} C\)$ model from part 1 & 2.

Part 4

The probability of observing $\({{params.temp}} ^{\circ} F\)$ temperature of higher in June in LA is 0.1056. Compare the answer with the one in part 3 of this question. Are you surprised? Explain.

Answer Section

Part 5

Estimate the IQR of the temperatures (in $\(^{\circ} C\)$) in June in LA.

Attribution

Problem is from the OpenIntro Statistics textbook, licensed under the CC-BY 4.0 license.