For a given day, temperature can be recorded as hot, mild and cold while weather can be sunny or cloudy. The probability that the temperature is hot, mild and cold are .15, .55 and .30, respectively. Probability that the weather is sunny if the temperature is hot is .67, if the temperature is recorded mild is.36, and if the temperature is cold is.33. Show all the steps including identification of what formulas/properties you used. Points will be deducted from answers if only the final answer is provided. (a) List all probabilities given in this problem, expressed in terms of events that you define.
(b) What is the probability that it is a sunny day?
(c) Given that the weather is sunny, what is the probability that the temperature is hot? mild? cold?
(d) Given that the weather is cloudy, what is the probability that the temperature is hot? mild? cold?
(e) Is the cloudy weather independent of hot weather?

Find the balance at the end of 4 years if 1000 is deposited at the rate of

Which is the equation of a line perpendicular to the line with the equation 3x+4y=8

(20 points) a bank has been receiving complaints from real estate agents that their customers have been waiting too long for mortgage confirmations. the bank prides itself on its mortgage application process and decides to investigate the claims. the bank manager takes a random sample of 20 customers whose mortgage applications have been processed in the last 6 months and finds the following wait times (in days): 5, 7, 22, 4, 12, 9, 9, 14, 3, 6, 5, 15, 10, 17, 12, 10, 9, 4, 10, 13 assume that the random variable x measures the number of days a customer waits for mortgage processing at this bank, and assume that x is normally distributed. 2a. find the sample mean of this data (x ě…). 2b. find the sample variance of x. find the variance of x ě…. for (c), (d), and (e), use the appropriate t-distribution 2c. find the 90% confidence interval for the population mean (îľ). 2d. test the hypothesis that îľ is equal to 7 at the 95% confidence level. (should you do a one-tailed or two-tailed test here? ) 2e. what is the approximate p-value of this hypothesis?