Answer: 0.70
Step-by-step explanation:
Given : The random variable X, representing the number of accidents in a certain intersection in a week, has the following probability distribution:
x 0 1 2 3 4 5
P(X = x) 0.20 0.30 0.20 0.15 0.10 0.05
Using the above probability distribution , the the probability that in a given week there will be at most 3 accidents is given by :_
Hence, the required probability = 0.70
Given Information:
Population mean = p = 60% = 0.60
Population size = N = 7400
Sample size = n = 50
Required Information:
Sample mean = μ = ?
standard deviation = σ = ?
Answer:
Sample mean = μ = 0.60
standard deviation = σ = 0.069
Step-by-step explanation:
We know from the central limit theorem, the sampling distribution is approximately normal as long as the expected number of successes and failures are equal or greater than 10
np ≥ 10
50*0.60 ≥ 10
30 ≥ 10 (satisfied)
n(1 - p) ≥ 10
50(1 - 0.60) ≥ 10
50(0.40) ≥ 10
20 ≥ 10 (satisfied)
The mean of the sampling distribution will be same as population mean that is
Sample mean = p = μ = 0.60
The standard deviation for this sampling distribution is given by
Where p is the population mean that is proportion of female students and n is the sample size.
Therefore, the standard deviation of the sampling distribution is 0.069.