Answer:
a. Mean = 4.5, Standard Deviation = 1.775
b. 0.0152
Step-by-step explanation:
Given
n = 15 purchasers
p = Success = 30%
p = 0.3
q =Failure = 70%
q = 0.7
a.
Mean = np
Mean = 15 * 0.3
Mean = 4.5
Standard Deviation = √Variance
Variance = npq
Variance = 15 * 0.3 * 0.7
Variance = 3.15
Standard Deviation = √3.15
Standard Deviation = 1.774823934929884
Standard Deviation = 1.775 ---------- Approximated
b.
The probability that the number who want new copies is more than two standard deviations away from the mean value
Standard Deviation = 1.775
Mean = 4.5
2 Standard Deviation and Mean = 2 * 1.775 + 4.5
= 3.55 + 4.5
= 8.05
P(X>8.05) = P(9) + P(10) +........+ P(15)
Using the binomial distribution
(p + q) ^ n where p = 0.3, q = 0.7 , n = 15
Expanding (p+q)^n where n = 15 and r > 8
We have
15C9 p^9 q^6 + 15C10 p^10 q^5 + 15C11 p^11 q⁴ + 15C12 p^12 q³ + 15C13 p^13 q² + 15C14 p^14 q + p^15
= 5005 (0.3)^9 (0.7)^6 + 3003 (0.3)^10 (0.7)^5 + 1365 (0.3)^11 (0.7)⁴ + 455 (0.3)^12 (0.7)³ + 105 (0.3)^14 (0.7)² + 15 (0.3)^14 (0.7) + 0.3^15
=0.015234
