Question

Find the indicated probability. Round to the nearest thousandth. Points: 5 20) In a batch of 8,000 clock radios 5% are defective. A sample of 7 clock radios is randomly selected from the 8,000 and tested. The entire batch will be rejected if at least one of those tested is defective. What is the probability that the entire batch will be rejected? Show your work below. A) 0.698 B) 0.302 C) 0.0500 D) 0.143 Estimate the indicated probability. Points: 5 21) A product is manufactured in batches of 120 and the overall rate of defects is 5%. Estimate the probability that a randomly selected batch contains more than 6 defects. probability Explain how you found the answer. Use the given data to find the minimum sample size required to estimate the population proportion. Points: 5 22) Margin of error: 0.027; confidence level: 95%; p and q unknown minimum sample size Show your work.

i need help with all 3 please

Answer 1

P = 0.08 20) let, x be the no of clock radios are defectives. probability of success je probability of Clock roadios are defective now, probability of failure, 92.1-P = 01959 probability or clock radios are not defective Here, n=7 XN B (n=7, p=005 os) we know that it X NB1n, p) then its pmf is given by p(x=x) = (2) pq co x=011 2. ospel, P+9=1 so.w Here, XWB (n = 7, P 20.05) then its pmf is given by one 7-02 7 ; x = 0, 1, 2 anos 7 Also given that, the entire batch will be rejected if at least of those tested is defective a now, we have to find the probability that the entire batch will be rejected, je PCX7,1) - |- P(x1) = PCXzo) P(x:o) (0) Coosjº (0-9537-4 .:P(820) = 0.6983 - . P(X711) 1-0.6983 P(x711) Anso 10 0.502 0.302 CS

cannot use binomial distribution 21) let x be the no.of defect in spandomly selected batches. given that, sample size, n=120 prob. of defects, p=0.05 Heren is large hence we we use poisson distribution with parameter, danp. .:): 120 X 0.05 Here, DP75 we know that, if you poisson (d) then its spmf is given by p(x-x): el de bria of 3 X 2011; 29 R! so.co d F10 Here, fanp=5 ع کیا .: P(x= x) = é o coje :23 071,- al now I have to find the probability that a batch contains more than 6 defects randomly selected ie P(x>0) -|- P(X KG) .: P( x86) = P(x=0) +plX-1) + P(X=2) +P (83) + P(x4) + P( X = 5) + P 3: ) | PlXr6 = 6. 60630 p(876) = 1- 0.60630 P (X76) = 0.3937] ICS

22 we know that, margin of error to estimate the population proportion (p) ia MOE = 2212 given that, osto margin of error= 0.027 significance level ld) = .? Zelle - Izoros mol - 1095 Oos (5%) 0 2 21 beti Ô = 0.5 in order to find mo E 2212 å = 1-² = o.s minimum sample size we considee, P 99 n 0.027: 196 0.5xor 0.027 2 0.98 6 dñ= 0.98 0.027 55= 36.2963 ..n= (36:2963)² 23 X 1 i n = 1317, 4211 ñ 1317, .: The required sample size to estimate the population proportion is 1317. CIS