l T-Mobile LTE * 13% 7:32 PM math.csi.cuny.edu eBWorK MATHEMATICAL ASSOCIATION O

Question

l T-Mobile LTE * 13% 7:32 PM math.csi.cuny.edu eBWorK MATHEMATICAL ASSOCIATION OF AMERICA Logged in as amakkisr3102 Log Out@ webwork math31 1-14270ohnson-f17 16.centrallimittheorem 1/1 16.CentralLimitTheorem 1 Problem 1 Prev Up Next (1 pt) Use normal approximation to estimate the probability of passing a true/false test of 60 questions if the minimum passing grade is 80% and all responses are random guesses. Preview Answers Submit Answers You have attempted this problem 0 times. You have unlimited attempts remaining. Email instructor

Explanation / Answer

1. Let X be the random number of correct answers out of n=60 true/false questions. The probability a single question is answered correctly is p=0.5. Thus the exact distribution of X is binomial: XBinomial(n=60,p=0.5).

But we need to approximate this as a normal distribution as the calculation would be tedious.

So we approximate X as a normal distribution with mean = n x p = 60 x 0.5 = 30 and standard deviation = sqrt (n x p x (1-p) ) = sqrt (60 x 0.5 x 0.5) = sqrt (15) = 3.8729

To get a passing grade of 80%, the number of correct answers required = 0.8 x 60 = 48

So, P(X>48) = P(Z > (48-30)/3.8729) = P(Z>4.64758) = 1 - 0.999998322 = 1.67844 x 10^(-6) is almost 0

2. n = 250, p, probability of a person arriving =0.9, q = 1-p = 1-0.9 = 0.1

This is a binomial distribution with mean = n x p = 250 x 0.9 = 225 and standard deviation = sqrt (n x p x q) = sqrt (250 x 0.9 x 0.1) = 4.7434

P (X>240) = P (Z> (240-225)/4.7434)) = P (Z> 3.162278) = 1-0.99921 = 0.00079

Related Questions

Navigate

• Browse (All)
• Browse L
• Subjects

---

---

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