In any given day the air quality in a certain city is either good or bad.  Records show that when the air  quality is good on one day, then there is a 95% chance that it will be good the next day, and when the air quality is bad on one day, then there is 45% chance it will be bad the next day. a. Give the transition  matrix. b.  if the air quality is good today, what is the probability it will be good two days from now? c.  if the air quality is bad today, what is the probability it will be bad three days from now? d.  if the there is 20% chance the air quality is good today, what is the probability it will be good tomorrow

A store specializing in mountain bikes is to open in one of two malls. If the first mall is​ selected, the store anticipates a yearly profit of $825,000 if successful and a yearly loss of $275,000 otherwise. The probability of success is 1/2. If the second mall is​ selected, it is estimated that the yearly profit will be $550,000 if​ successful; otherwise, the annual loss will be $165,000. The probability of success at the second mall is 3/4. What is the expected profit for both mall 1 and 2? Which mall should be chosen in order to maximize the expected​ profit?

Parts d and e

The owner of a chain of mini-markets wants to compare the sales performance of two of her stores, Store 1 and Store 2. Sales can vary considerably depending on the day of the week and the season of the year, so she decides to eliminate such effects by making sure to record each store's sales on the same 12 days, chosen at random. She records the sales (in dollars) for each store on these days, as shown in the table below. 5 6 7 Day Store 1 Store 2 1 Difference (Store 1 - Store 2) Send data to calculator ✓ 2 3 786 878 827 645 708 500 699 140 Yes No 4 646 802 712 579 527 367 76 115 66 181 133 8 (a) State the null hypothesis H and the alternative hypothesis H₁. H:D H₁:0 (b) Determine the type of test statistic to use. Type of test statistic: (Choose one) ▼ 970 9 10 11 12 618 679 762 635 271 572 324 215 698 530 Based on these data, can the owner conclude, at the 0.05 level of significance, that the mean daily sales of the two stores differ? Answer this question by performing a hypothesis…