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Ip ?69% , Sun Jul 15 9:28 PM Do Homework- Maira Arshad Secure https: aspx?homeworkld-487246818&questionld; 10&flushed; false&cld; 5052971&centerwi..; MTH 241-E56A-Statistics I-Second 8-Week (1) Maira Arshad& I 7/15/18 9:28 PM Other Bookma Homework: HW Section 6.6 Score: 0 of 1 pt Save 44 of 10 (8 completel Score: 60%, 6 of 10 pts e 6.6.15 Question Help * (a)With n = 13 and p=0.6 find P(at least 11)using a binomial probabily table (b) If rp 25 and nq 25, also ostate Pat least 11) by using the nomal di bdn as an approximation to the binomial distribution; if np5 or nq

Explanation / Answer

Solution:- Given that n = 13, p = 0.6

(a) P(at least 11) = 0.058
  
=> P(X >= 11) = P(11)+P(12)+P(13) = 0.0453 + 0.0113 + 0.0013 = 0.0579 = 0.058

(b)
The number of samples n = 13.

Probability of success event p = 0.6

Probability of failure event q = 1 - p = 1 - 0.6 = 0.4

First find np = 13*0.6 = 7.8, np > 5

nq = 13*0.4 = 5.2, nq > 5

Now np > 5 and nq > 5 then estimate the indicated probability using normal distribution.

mean = np = 13*0.6 = 7.8

Standard deviation = sqrt(13*0.6*0.4) = 1.7664

P(x >= 11) = P(Z > (11.5 - 7.8)/1.7664)
= P(Z > 2.0946)
= 0.0183

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