One of the employees at the M&Ms factory in Hackettstown, Pennsylvania claims that all M&Ms factories in the U.S. produce an equal number of each of the six colors of M&Ms. We will investigate this claim in the following questions. Since it is not practical for us to visit each M&Ms factory in the U.S., we will rely sample data. Assuming the M&Ms factory employee is correct and all six colors of M&Ms are equally distributed, we will use the population proportion p = 1/6 = 0.1667.bon a. A student group decides to use a sample size of n = 100 M&Ms. Check th normality conditions. Is it reasonable to use a normal distribution for this sample size? Document your calculations. M3M sold to noihogong ect boda rato aniqmas ynem won bris phibnoquemoo b. In the random sample of n = 100 M&Ms, the students find that 21 are blue M&Ms. What is the sample proportion ? #n sonri c. Calculate the standard error: Mart MAM ab ort stof evode argang er ni anoneneltib d. Construct a 95% confidence interval. Senasis elgimuse MAM 01 Innbu ribes sono ima di odinioa bounna one oqeria M&M candies are sometimes produced in special colors for holiday bags, but the usual colors are orange, red, yellow, green, blue and brown. Isamon eau of elderoesma affibriga ylilamor Last semester, students in a statistics class at LMC collected random samples of M&Ms candy and counted the proportion of blue M&Ms in each sample, in order to estimate the true proportion of blue M&Ms in the population of all M&Ms. Here are the results. These dot plots show the proportion of blue M&Ms, corresponding with different sample sizes n and how many samples each student collected. mold en 15 fart brit n=10 M&Ms sample size each student sampled once 0 0.1 02 0,3 0.4 n=20 M&Ms sample size each student sampled twice 0 18M 001 = n to elgmaa mobne 0.10 0.20 0.30 0.40 n=100 M&Ms sample size each student sampled three times 0 0.09 0.18 0.27 e. Write a sentence interpreting the 95% confidence interval. eelamma brs alou woled betulbin e eo of ins f. A friend not in statistics class claims that 1/3 or about 33% of M&Ms are blue. Based on the confidence interval you constructed, does the friend's claim seem possible? Explain your reasoning with complete sentences.