this is statistics course and I need help with answering these questions. I attached formulas in case you can use it as a reference.Thank you

II. Probability PM U B) = PM) + P(B] Pull n B) m = Lag?) Var-(X) = 0% = 2m 11:39-19: If X has a binomial distribution with parameters :1 and p, then: P(X = k) = (:)pt(1_ 13)": \"3:74!\" If E la the mean ofa random sample ofsize n from an innite population with mean p and standard deviation 0', then: T 0' \"i=7: III. Inferential Statistics Standardized test statistic: statistic - parameter standard deviation of statistic Confidence interval: statistic + (critical value) . (standard deviation of statistic) Single-Sample Statistic Standard Deviation of Statistic Sample Mean Sample Proportion p(1 - p) n Two-Sample Statistic Standard Deviation of Statistic Difference of sample means n2 Special case when 0 =02 Difference of P (1 - PI) + P2 (1 - P2) sample proportions n 1 n2 Special case when P = P2\fO 0.970 D Question 39 1 pts Janet surveyed 300 students at a school and recorded each student's preference of ice-cream between chocolate, vanilla, and strawberry, as well as the gender of each student. Of the 125 females surveyed, 75 preferred chocolate ice cream. Assuming ice-cream flavor preference and gender are independent, how many male students would you expect to prefer chocolate ice cream? 50 O 105 O 100 125 O 175O 0.570 O 0.714 D Question 38 1 pts A quality inspector at a tire factory examines outgoing shipments of tires by randomly selecting one tire at a time, until one is found to be defective. Suppose that 3% of tires are known to be defective. What is the probability that the 3rd tire the inspector examines is the first sample to be found defective? O 0.028 O 0.059 O 0.120 O 0.940 O 0.970 Question 39 1 ptsO 0.75 O 0.94 D Question 37 1 pts In the United States, most space-bound rockets are launched from Cape Canaveral, Florida. During the month of May, there is a 20 percent chance of heavy rain, in which case the launch will be postponed. If it does not rain, there is only a 7 percent chance that a flight will be postponed due to mechanical failure. Suppose, NASA is scheduled to launch a satellite into orbit in the month of May. What is the probability that the launch will be postponed for at least one of these reasons? O 0.176 O 0.256 O 0.470 O 0.570 O 0.714Question 36 1 pts The distribution of t-shirt sizes in a box is as follows. X- XX- Size Small Medium Large Large Large Proportion 0.2 0.3 0.25 0.15 0.1 If two t-shirts are randomly drawn from the box with replacement, what is the probability that both of them are small or medium? O 0.06 O 0.25 O 0.50 O 0.75 O 0.94