Q1) Shoe manufacturer is known to create 5% of shoes as defective.  ShoeFit store newly ordered 300 pairs from this manufacturer.  Let x be number of defective shoes in order received by ShoeFit store.

i) Write a formula for probability distribution of x.

ii) Compute  a)  P(x ≤ 5)             b)  P(x ≤ 20)

iii) Give the expected value and standard deviation of defective shoes in the ShoeFit store order.

iv) Playing Pick 4, continued The Wisconsin version of Pick four pays out $5000 on a $1 bet if your number matches winning number exactly. It pays $200 on $1 bet if digits in your number match those of winning number in any order. You select which of these two bets to make. On average over many bets, your winnings will be mean amount won = payout amount × probability of winning. Determine the mean payout amounts for these two bets? Is one of the two bets a better choice?