Question

Please help me find the answers to the last two problems step by step.

The average playing time of compact discs in a large collection is 35 minutes, and the standard deviation is 5 minutes. (a) What value is 1 standard deviation above the mean? 1 standard deviation below the mean? What values are 2 standard deviations away from the mean? 1 standard deviation above the mean 1 standard deviation below the mean 30 2 standard deviations above the mean 45 2 standard deviations below the mean (b) Without assuming anything about the distribution of times, at least what percentage of the times are between 25 and 45 minutes? (Round the answer to the nearest whole number.) At least 75 (c) Without assuming anything about the distribution of times, what can be said about the percentage of times that are either less than 20 minutes or greater than 50 minutes? (Round the answer to the nearest whole number.) No more than 11 % (d) Assuming that the distribution of times is normal, about what percentage of times are between 25 and 45 minutes? (Round the answers to two decimal places, if needed.) 95.44 Less than 20 min or greater than 50 min? X % 0.26 Less than 20 min? 0.13 %

Answer 1

Here, average (M) = 35 minutes Standard deviation (O) = 5 minutes P(less than 20 min or greater than 50 min) = P(less than 20 min) +PC greater than 50 min) =P ( x<20 min ) + P(x750 min) < P ( x - 21 20-35) + P ( x 50 35) = P(Z2-3) +P(E73) = (1-P(213)) + ( +-P(Z(3)) = (1 - 0.9987)+(1-0.9983) = 0.0026 *100 = 26.4 1. Less than 20 min or greater than 50 min 26 %. and p( Less than 20 min) Ep(4620) =P ( x-bilde 20135 ) =P(76-3) -pl Z(-3) I = 13% -0.0013 * 100 than 20 min. 13% less