The z-scores of the test results of a sample of 43 students follow the T-distribution with 42 degrees of freedom. Let X be the z-score of a randomly selected student. 1. Describe the distribution of X: X-T✓ ✓ (df-42 2. Use the random variable notation to express symbolically each of the following: P(X<-1.7)=0.05✓ The probability of an event in which the z-score of a randomly selected student is less than -1.7 is equal to 0.05. X<0 P(X<2) student is less than 2. ✓An event in which the z-score of a randomly selected student is less than 0. The probability of an event in which the z-score of a randomly selected 3. Use technology to find the probability that the z-score of a randomly selected student is: i. less than 0: ii. more than 2: iii. between -1 and 0.7: iv. more than 9.6: v. less than 12.3: 4. Find the 2-th percentile: 12% (round the answer to 2 decimal places) (round the answer to 2 decimal places) (round the answer to 2 decimal places) (round the answer to 2 decimal places) (round the answer to 2 decimal places) (round the answer to 2 decimal places)

Complete (D)

Assume that the amounts of weight that male college students gain during their freshman year are normally distributed with a mean of u 1.3 parts (a) through (c) below. a. If 1 male college student is randomly selected, find the probability that he gains between 0 kg and 3 kg during freshman year. The probability is (Round to four decimal places as needed.) b. If 16 male college students are randomly selected, find the probability that their mean weight gain during freshman year is between 0 kg and 3 kg. The probability is (Round to four decimal places as needed.) c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30? OA. Since the weight gain exceeds 30, the distribution of sample means is a normal distribution for any sample size. OB. Since the original population has a normal distribution, the distribution of sample means is a normal distribution for any sample size. and a standard deviation of a 5.1 kg. Complete OC. Since the…

Please solve the screenshot, (a) and (b) only. The answer for (b) is not 0.2!

Solve for D

he chance of an IRS audit for a tax return with over $25,000 in income is about 2% per year. We are interested in the expected number of audits a person with that income has in a 10-year period. Assume each year is independent. Give the distribution of X.X ~