Answer:
Step-by-step explanation:
Use the normal approximation to the binomial distribution
mean µ = np
standard deviation σ = √npq
Where,
n is sample size
p is probability of success.
q is probability of failure
Given that
q = 6% =0.06
Then, p = 1-q = 1-0.06 = 0.94
Therefore:
µ = pn
µ = 0.94n
Also
σ = √npq
σ = √(n)(0.94)(0.06)
σ = √(.0564n)
Using z-scores:
z = (x — µ )/σ
Using the data above
1.645 = (160 — 0.94n)/√(0.0564n)
Cross multiply
1.645√0.0564n = 160—0.94n
Square both sides
1.645²× 0.0564n = (160-0.94n)
0.153n=25600— 300.8n + 0.8836n²
0.8836n²-300.8n-0.153n +25600=0
0.8836n² — 300.953n + 25600 = 0
Using quadratic formula method.
a = 0.8836 b = -300.953 c = 25600
n = [-b±√(b²-4ac)]/2a
n = [--300.953±√((-300.953)²-4×0.8836×25600)] / (2 × 0.8836)
n = [300.953±√(92.07)]/1.7672
n = (300.953±9.6)/1.762
n = (300.953-9.6)/1.762
n = 168.22
Or
n = (300953+9.6)/1.762
n = 176.25
The maximum number of reservation is approximately 168.
