Question

1. Let X be a normal random variable with mean 16. If P(X < 20) 0.65, find the standard deviation o. 2. The probability that an electronic component will fail in performance is 0.2 Use the normal approximation to Binomial to find the probability that among 100 such components, (a) at least 23 will fail in performance. X 26) (b) between 18 and 26 (inclusive) will fail in performance. That is find P(18 3. If two random variables X and Y have the joint density (6r+3y) for 0<z<1, 0 <y<1 { f(r.y) elsewhere (a) Find k (b) Find marginal density fi() and fz). (c) Are X and Y independent? (d) Find P(0<Y< 5) (e) Find i. an expression for (rly); ii. an expression for fi(0.5); 4. If the distribution of the weights of all men traveling by air between Washington and Toronto has a mean of 165 pounds and an standard deviation of 18 pounds, what is the probability that the combined gross weight of 49 men traveling on a plane between these two citics is less than 8200 pounds? 5. The dean of a college wants to use the mean of a random sample to estimate the average anount of time students take to get from one class to the next, and she wants to be able to assert with 90% confidence that the error is at most 0.15 minute. If it can be presumed from experience that o-1.8 minutes, how large a sample will she have to take? 6. Thirty six bearings made by a certain process have a mean diameter of 0.6 em and are taken from a population with standard deviation a 0.05 em. Construct a: (a) 95% confidence interval for the population mean diameter of the bearings (b)90% confidence interval for the population mean diameter of bearings made by this process

Answer 1

0.65 rom Probiy ス= 0.385 normalishi butm ut Given 20 0. 38S- 2o-16 o. 39 An answe one