LA weather, Part I. The average daily high temperature in June in LA is 77◦F with a standard deviation of 5◦F. Suppose that the temperatures in June closely follow a normal distribution.
(a) What is the probability of observing an 83◦F temperature or higher in LA during a randomly chosen day in June?
(b) How cool are the coldest 10% of the days (days with lowest average high temperature) during June in LA?
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)× 5
(a) Write the probability model for the distribution of temperature in ◦C in June in LA.
(b) 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).
(c) 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.
(d) Estimate the IQR of the temperatures (in ◦C) in June in LA.
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