Excel Output of the Binomial Distribution with n = 24, p = 0.15, and q = 0.85 Binomial distribution with n = 24 and p = 0.15 JAWN- OX P(X=x) 0.0202 0.0857 0.1739 0.2251 0.2085 0.1472 (Note: The Excel output may not include all of the x values.) (a) Find P(x = 0), that is, find the probability that none of the randomly selected golf balls exceeds 1.62 oz. in weight. (Use table values rounded to 4 decimal places for calculations. Round your answer to 4 decimal places.) P(x = 0) 0.0202 (b) Find the probability that at least one of the randomly selected golf balls exceeds 1.62 oz. in weight. (Use table values rounded to 4 decimal places for calculations. Round your answer to 4 decimal places.) P(x 2 1) 0.9798 (c) Find P(x s 3). (Use table values rounded to 4 decimal places for calculations. Round your answer to 4 decimal places.) P(X 5 3) 0.5049 0 (d) Find P(x 2 2). (Use table values rounded to 4 decimal places for calculations. Round your answer to 4 decimal places.) P(x 2 2) 0.7547 (e) Suppose that 2 of the 24 randomly selected golf balls are found to exceed 1.62 oz. Using your result from part d, do you believe the claim that no more than 15 percent of this brand of golf balls exceed 1.62 oz. in weight? No , the probability of this result is |small if the claim is true.15. You did not receive full credit for this question in a previous attempt Suppose that x is a binomial random variable with n = 5, p = 0.2, and q = .80. (b) For each value of x, calculate p(x). (Round final answers to 4 decimal places.) p(0) = 0.3276 , p(1) = 0.4096 p(2) = 0.2048 , p (3) = 0.0512 p(4) = 0.0064 , p(5) = 0.0003 (c) Find P(x = 3). (Round final answer to 4 decimal places.) P(X=3) 0.0512 (d) Find P(x 2). (Do not round intermediate calculations. Round final answer to 4 decimal places.) P (x > 2 ) 0.0579 (h) Use the probabilities you computed in part b to calculate the mean ,, the variance, or , and the standard deviation, ox, of this binomial distribution. Show that the formulas for Hx , or , and ox given in this section give the same results. (Do not round intermediate calculations. Round final answers to J, in to 2 decimal places, o , and ox in to 4 decimal places.)(h) Use the probabilities you computed in part b to calculate the mean ux, the variance, of , and the standard deviation, ox, of this binomial distribution. Show that the formulas for Hx , or , and ox given in this section give the same results. (Do not round intermediate calculations. Round final answers to J, in to 2 decimal places, o x and ox in to 4 decimal places.) Px OF 0.8 0.8944 (i) Calculate the interval [, 1 20,]. Use the probabilities of part b to find the probability that x will be in this interval. Hint: When calculating probability, round up the lower interval to next whole number and round down the upper interval to previous whole number. (Round your answers to 4 decimal places. A negative sign should be used instead of parentheses.) The interval is | -0.7888 2.7888 P( 0.9772 S XS 0.0526 ) 0.942618_ Award: 1 out of 3.00 points Sound City sells the CleerTone400 satellite car radio. For this radio. historical sales records over the last 100 weeks show 7 weeks with no radios sold 15 weeks with one radio sold. 17 weeks With two radios sold, 42 weeks with three radios sold, 12 weeks with four radios sold. and 7 weeks with ve radios sold. Calwlale u," :13. end a,\" of x, the number ofCleerTone-4Gn radios sold at Sound City during a week using the estimated probability distribution. {Round your answers to 2 decimal places.)
