Question

Find the indicated binomial probability. A company manufactures calculators in batches of 64 and there is a 4% rate of defects. Find the probability of getting exactly 5 defects in a batch 0.7808 0.0018 2141 0.0702 None of these Question 4 10 pts Find the area under the standard normal curve. P(-2.13<Z<1.16) Round to four decimals. 0.7256 0.8604 0.6713 .9712 None of these

Answer 1

Question 3 The company manufactures calculates n = 64 number of batches and there is a p=0.04 (or 4%) rate of defects. Then we know that our distribution follows a binomial distribution with n = 64 and p = 0.04 or X ~ bin(n = 64, p = 0.04) where X is the number of defects. Then probability of getting exactly 5 defects in a batch is = = P[X = 5] p> (1 – p)n-5 64 0.04% (1 – 0.04)n-5 5 = 0.0702 Hence the probability of getting exactly 5 defects in a batch is 0.0702. n = 5 Question 4 We know that Z has a standard Normal curve i.e. Z ~ N(0,1). Then. P(-2.13 < Z < 1.16) P(Z < 1.16) – P(Z < -2.13) = $(1.16) – 0(–2.13) = $(1.16) - (1 - 0 (2.13)) = 0.877 – (1 – 0.9834) = 0.8604 Hence, P(-2.13 < Z < 1.16) = 0.8604.