You are to model the daytime temperature of the Mojave desert during the summer time. Temperatures in the desert are modeled to follow a normal distribution with µ = 102 Fahrenheit and variance σ 2 = 25 Fahrenheit. a. Write out the integral form of the probability that the temperature will be between 97 to 107 degrees Fahrenheit. Use pnorm functions in R,(pnorm(x, µ, σ)) or use empirical rule to compute numeric value. b. What is the probability that the temperature will be 120 degrees? What is the probability of the temperature being below 120? Write out integral form and use R (pnorm) to compute. c. Say X is the random variable that denotes the temperature during the desert day. What distribution does 0.55X-17.6 follow? State the type of distribution, and all parameters. d. Now say you relax the normality assumption from the model, and you observe 25 days temperatures (X1, X2, ..., X25) from some unknown distribution. What is the approximate distribution of the sample mean of these daily temperatures, X¯ = 1 n Pn i=1 Xi? State the approximate type of distribution and all parameters.