Give Probability

According to Masterfoods, the company that manufactures M&M's, 12% of peanut M&M's are brown, 15% are yellow, 12% are red, 23% are blue, 23% are orange and 15% are green. [Round your answers to three decimal places, for example: 0.123] Compute the probability that a randomly selected peanut M&M is not yellow. Compute the probability that a randomly selected peanut M&M is orange or yellow. Compute the probability that three randomly selected peanut M&M's are all red. If you randomly select two peanut M&M's, compute that probability that neither of them are red. If you randomly select two peanut M&M's, compute that probability that at least one of them is red.3. The heights of women in the fictional country of thsia follow a Normal distribution. You'd like to perform a hypothesis test to see if the average height of thsian women is significantly more than 61 inches. You select 8 women at random and measure their heights (in inches), which are recorded in the table below. '61'61'62-64'67I63'64[62 a. Find the mean and standard deviation of the heights in the sample. Use the correct symbols for this sample data. b. Wn'te hypotheses to test whether the population height is over 61 inches. c. Perform the calculations for the test. Please report the value of test statistic (t) and the p-value. d. Can we conclude the mean height of ghlgia women is significantly greater than 61 inches? Explain why or why not. (Use a = 0.05)