A majority of small businesses are owned by men. Suppose that only 30% of small businesses are owned by women. Suppose 15 small businesses are chosen at random and the number owned by women is recorded.

a) Verify that this is a legitimate probability distribution. HINT: In Excel, click on cell B18. Type "-sum(B2:B17)" to sum the values in the Probability column. b) Use Excel to create a probability histogram. Excel Highlight the cells containing the distribution. Click on the Insert tab at the top -> Recommended Charts > select appropriately. Identify the shape of the distribution: Skewed Symmetric Skewed Left Right c) On average, how many small businesses are expected to be owned by women? Use Excel and the formula for general discrete probability distributions, MNF Exxxx to answer this question HINT: In Excel, click on cell C2. Type "=A2*B2". Press Enter. Click back on C2, click and drag on the small square in the bottom right of the cell to auto-fill the remaining cells in the column with the product of to xxppxx for each value of xxThen sum the column. d) On average, how many small businesses are expected to be owned by women? Use the binomial formula for the mean, WHX nnpjo verify you get the same answer as in part (c). e) What is the probability that exactly 8 of the small businesses will be owned by women? f) What is the probability that 8 of the small businesses are not owned by women? g) What is the probability that between 4 and 8 of the small businesses will be owned by women