7. [-/10 Points] DETAILS MENDSTATC4 5.E.017. MY NOTES ASK YOUR TEACHER Find the mean / and standard deviation o for a binomial distribution with n = 100 and the following values of p. (Round your answers to two decimal places.) (a) p = 0.01 U= O= (b) p = 0.9 (c) p = 0.4 U = O = (d) p = 0.6 H = O= (e) p = 0.5 U =Car colour preferences change over the years and according to the particular model that the customer selects. In a recent year, 10% of all luxury cars sold were black. If 25 cars of that year and type are randomly selected, find the following probabilities. (Round your answers to three decimal places.) (a) At least five cars are black. (b) At most seven cars are black. (1:) More than four cars are black. (d) Exactly four cars are black. (e) Between three and five cars (inclusive) are black. (f) More than 21 cars are not black. Evaluate these probabilities. (Round your answers to four decimal places.) 4 3 CC (a) _x C 2 (33? a) C9 =: 3 A company has eight applicants for two positions: two women and six men. Suppose that the eight applicants are equally qualified and that no preference is given for choosing either gender. Let x equal the number of women chosen to fill the two positions. (a) Write the formula for p(x), the probability distribution of X. csc 2 O p(x) = forx = O, l, 2 8 C2 8 6 C C O p(x) =XHforx Ci 0,1,2 6 2 C C O p(x) =XHforx C: O, i,2,3,4, 5, 6, 7,8 2 6 C C2 0 p(x) = #forx C: H O H N 2 6 C C O p(x) = X+:_Xforx C 2 O, i,2,3,4, 5, 6, 7,8 (b) What are the mean u and variance 02 of this distribution? (Round your mean to one decimal place and your variance to two decimal places.) .1 = E MY NOTES ' ASK YOUR TEACHER ' I PRACTICE ANOTHER 11. [13 Points] MENDSTATC45tE.OS7. Seeds are often treated with a fungicide for protection in poor-draining, wet enVironments. In a small-scale trial prior to a large-scale experiment to determine what dilution of the fungicide to apply, four treated seeds and five untreated seeds were planted in clay soil and the number of plants emerging from the treated and untreated seeds were recorded. Suppose the dilution was not effective and only four plants emerged. Let X represent the number of plants that emerged from treated seeds. (Round your answers to three decimal places.) (a) Find the probability that X = 4. :l (b) Find P(X s 3). :I (c) Find P(2 s X s 3). :l Find PM 5 k) in each case. (Round your answers to three decimal places.) (a) n=20,p=0.15,k=2 0.405 a; n=15,.,p=07k= B _. 005 x n=10,,p=0.8 k=9 _. 375 X