The average daily high temperature in Los Angeles is μ = 70°F with a standard deviation of σ= 5° F. Suppose that the temperatures in June closely follow a normal distribution: that is, if we let X be the temperature of a randomly chosen day in June, we have that X ~ N(μ, σ2) Required:
a. What is the probability of observing an 83℉ temperature or higher during a randomly chosen day in June?
b. What is instead the probability of observing a temperature between 70°F and 80°F?
c. How cold are the coldest 10% of the days during June in Los Angeles?
d. Let Y be temperature of a randomly chosen day in June measured in Celsius degrees (°C) instead of Fahrenheit (℉) degrees: that is, Y = (X-32) x . Write the probability model for Y. (In other words what is the probability distribution of Y?)
e. What is the probability of observing a 28.33°C (which corresponds to 83°F) temperature or higher in June in Los Angeles?