Please answer the following ,, show all steps and formulas used. Thank you. In a
ID: 3248677 • Letter: P
Question
Please answer the following ,, show all steps and formulas used. Thank you.
In a process that manufactures bearings, 90% of the bearings meet a thickness specification. A shipment contains 500 bearings. A shipment is acceptable if at least 440 of the 500 bearings meet the specification. Assume that each shipment contains a random sample of bearings. c) What is the probability that between 270 and 280 out of 300 shipments are acceptable? d) What is the probability that 280 out of 300 shipments are acceptable?Explanation / Answer
f 90% of the the bearing meet a thickness specification.
Probability that at least 440 out of 500 meet the specification is 0.9190 (value is obtained using binomial formula = 1 - BINOM.DIST(440,500,0.9,TRUE))
Now p = 0.919, n = 300, q = 1-p
mean = np = 275.7039
std. dev. = sqrt(npq) = 4.7253
(C)
Now p = 0.919, n = 300, q = 1-p
mean = np = 275.7039
std. dev. = sqrt(npq) = 4.7253
P(270<X<280) = P((270-275.7)/4.7253 < z < (280-275.7)/4.7253) = P(-1.2063 < z < 0.91) = 0.70467
(D)
Here we can find the probability by using binomial
P(X=280) = 300C280 * p^280 * q^20 = 0.0594