Suppose that 48 of all hotel guests reuse towels instead of

Suppose that 48% of all hotel guests reuse towels instead of sending them to the laundry every day.

a.)In a random sample of 200 hotel guests, use the normal distribution to find the probability that fewer than 42% reused their towels.

b.)Show the sample size check that justifies the normal distribution for this problem.

Solution

a)
Proportion ( P ) =0.48
Standard Deviation ( sd )= Sqrt (P*Q /n) = Sqrt(0.48*0.52/200)
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
P(X < 0.42) = (0.42-0.48)/0.0353
= -0.06/0.0353= -1.6997
= P ( Z <-1.6997) From Standard Normal Table
= 0.0446                  
b)
For n=200
n*p>5, 200*0.48> 5 => 96>5
n*(1-p)>5, 200*0.52> 5 => 96>5
Can Use Normal Approximation