Question

pleasa solve questions 3,4 and 5

2. The time required to assemble a piece of machinery is a random variable having a normal distribution with 7.0 and a=1.5 minutes. What are the probabilities (and draw the region) that the assembly of a piece of machinery of this kind will take (a) at least 5 minutes; (b) anywhere from 4 to 8 minutes? 3. Draw the region and determine, (a) 02 (b) 3 (e) 0.15 3. Draw the region and determine, (a) z0.24 (b) 03s (e) 2o.15 4. If a random variable has the standard normal distribution, find the probability (and draw the region) that it will take on a value (a) greater than 1.65; (b) greater than -0.75 (c) between -1.25 and 2.25 (d) between -1.85 and 1.45 5. [2 points] In 2 out of 10 cases, material for bulletproof vests fails to meet puncture standards. If 100 specimens are tested, what does Chebyshev's theorem tell us about the probability of getting between 14 and 26 cases that fail to meet puncture standards?

Answer 1

5-7 P(X >5): P 5 o. 9o878 88 P(z> -3333) 8-7 = o.7 47573 P(z) (a) 2-o.706302/ Piz) -o.70 6302 (6) .5 = o.385 3.205 PIZ) -0-3853405 z -l.o3!4 33 O.1S ,o36433 o.04947 ? z >.65) = 0 :oi q 47 (a) 165 F0.7733 7 -o. 7s) J 8821 z I.s) P- 1.85 4 0894314 (d) 1,85