The answer is:
The explanation is shown below:
1. Cynthia rounds the number, which is identified as , to one decimal place and the result is 6.3.
2. Based on this, we know that could have been between 6.25 and 6.35. Therefore, the error interval for
is given by:
Where indicates that the value 6.25 is included and
indicates that the value 6.35 is not included (Because if
had been exactly 6.35, Cynthia would round up to 6.4).
Let X be the number of female employee. Let n be the sample size, p be the probability that selected employee is female.
It is given that 45% employee are female it mean p=0.45
Sample size n=60
From given information X follows Binomial distribution with n=50 and p=0.45
For large value of n the Binomial distribution approximates to Normal distribution.
Let p be the proportion of female employee in the given sample.
Then distribution of proportion P is normal with parameters
mean =p and standard deviation =
Here we have p=0.45
So mean = p = 0.45 and
standard deviation =
standard deviation = 0.0642
Now probability that sample proportions of female lies between 0.40 and 0.55 is
P(0.40 < P < 0.45) =
= P(-0.7788 < Z < 1.5576)
= P(Z < 1.5576) - P(Z < -0.7788)
= P(Z < 1.56) - P(Z < -0.78)
= 0.9406 - 0.2177
= 0.7229
The probability that the sample proportion of females is between 0.40 and 0.55 is 0.7229
