Suppose that 30% of all telephone calls at work are for personal reasons. If a random sample of 15 is taken, let X be the number of personal calls. The standard deviation of the # of personal calls is:
Standard deviation = √npq
n = sample size = 15
p = .30
q = 1 - p = .70
I'll let you take it from here.
A telephone exchange operator assumes that 7% of the phone calls are wrong numbers.
If the operator is correct, what is the probability that the proportion of wrong numbers in a sample of 624 phone calls would differ from the population proportion by greater than 3% ? Round your answer to four decimal places.
To find the standard deviation of the number of personal calls, we first need to calculate the variance.
The variance (σ²) of a random variable is calculated using the formula:
σ² = np(1 - p)
Where:
- n is the sample size
- p is the probability of success (in this case, the probability of a personal call)
In this scenario, the probability of a personal call is 30% or 0.3, and the sample size is 15.
So, the variance is:
σ² = 15 * 0.3 * (1 - 0.3)
Simplifying the equation:
σ² = 15 * 0.3 * 0.7
σ² = 3.15
Now, to find the standard deviation (σ), we take the square root of the variance:
σ = √(3.15)
Calculating the square root:
σ ≈ 1.775
Therefore, the standard deviation of the number of personal calls is approximately 1.775.