Question

a. The width of bolts of fabric are normally distributed with a mean of 950 millimetres and a standard deviation of 10 millimetres. What is the probability that a randomly chosen bolt has a width between 947 and 958 millimetres? (3 marks) ii. What is the appropriate value for such that a randomly chosen bolt has a width less than C with probability 0.8531? (3 marks) b. A certain diagnostic test for a certain disease is said to be 90% accurate in that, if an animal has a disease, the test will detect it with probability 0.9. Also if an animal does not have the disease, the test will report that the animal does not have it with probability 0.9. Only 1% of the animal population has the disease in question. If an animal is selected at random from the population and the test indicates that the animal has the disease, what is the probability that the animal does, in fact, have the disease? (4 marks)

Answer 1

Bunlad Date Pago - het x-width X ~ N 1 M, 62 ~ N (950, 100 (a) p( gu1cxc 958) Transform into Normal Standard- P ( 947-950, X-4 < 958 - 950 ) P-2 10 221 P (-0.3<2 <0.8) by a table vabe. = 0.1179 + 0. 2881. = 0.406 PLXLC) = 0.8531 -PTX-4 < ) = 0.853) 1/2 L (M) = 0.6531 Plz<-1980) = 0.853/ by 2 valee table- .3531 C-950 1.05 To = 960.5 c = 10.5+950