In an experiment, 3737% of lab mice cells exposed to chemically produced cat Mups responded positively (i. e., recognized the danger of the lurking predator). Consider a sample of 200200 lab mice cells, each exposed to chemically produced cat Mups. Let x represent the number of cells that respond positively. Complete parts a through d below. a. Explain why the probability distribution of x can be approximated by the binomial distribution. There are 200200 identical trials. For each trial, there are two possible outcome(s). The probability of each possible outcome is different for each trial, and the trials are all independent. b. Find E(x) and interpret its value, practically. E(x)equals=7474 (Round to the nearest whole number as needed.) Interpret this value. Choose the correct answer below. A. At most E(x) cells out of 200200 will respond positively in similar experiments. B. On average E(x) cells out of 200200 will respond positively in similar experiments. C. At least E(x) cells out of 200200 will respond positively in similar experiments. D. Exactly E(x) cells out of 200200 will respond positively in similar experiments. c. Find the variance of x. The variance of x is 46.6246.62. (Round to two decimal places as needed.) d. Give an interval that is 95% likely to contain the value of x. Using the empirical rule, x is likely in the interval (nothing, nothing). (Round to one decimal place as needed.)