1.An electric store has received a shipment of 20 table radios that have connections for the iPhone. 12 of these have 2 slots and the others have a single slot. Suppose, 6 of the 12 radios are randomly selected to store. Let, X be the number of stored radios with two slots. a. What kind of s distribution does X have? (include all the values of the parameters) b. Compute, P(X ≤ 3 ). c. Calculate the mean and standard deviation of X. d. Calculate the probability that X exceeds its mean value by less than one standard deviation. e. Plot the Histogram of X and comment on the shape of the distribution.
2.The records of an Italian shoe manufacturer show that 20% of the shoes are defective. Assume that selection of shoes follow a Bernoulli trial. a. If a manufacturer inspects 15 shoes randomly, what is the probability that at most two shoes are defective? b. If a manufacturer wants to find 6 non defective shoes, what is the probability that 12 shoes have to be inspected? c. Find the expected number of inspected shoes to find 6 non defective shoes.
