Although errors are likely when taking measurements from photographic images, th

Question

Although errors are likely when taking measurements from photographic images, these errors are often very small. For sharp images with negligible distortion, errors in measuring distances are often no larger than .0004 inch. Assume that the probability of a serious measurement error is .05. A series of 150 independent measurements are made. Let X denote the number of serious errors made.

a) In finding the probability of making at least one serious error, is the normal approximation appropriate? If so, approximate the probability using this method.

b) Approximate the probability that at most three serious errors will be made.

Explanation / Answer

p = 0.05, n = 150, q = 1 - p = 0.95

(a) np and nq are both greater than 5, so normal approximation can be used

= np = 150 * 0.05 = 7.5, = (npq) = (150 * 0.05 * 0.95) = 2.67

z = (x - )/ = (1 - 7.5)/2.67 = -2.4344

P(x 1) = P(z > -2.4344) = 0.9925

(b) z = (3 - 7.5)/2.67 = -1.6854

P(x 3) = P(z < -1.6854) = 0.046

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.