Individuals who have a certain gene have a 0.50 probability of contracting a certain disease. Suppose that 1,940 individuals with the gene participate in a lifetime study. What is the standard deviation of the number of people who eventually contract the disease? Round your answer to 2 decimal places.
standard deviation = √npq
n = sample size = 1940
p = 0.50
q = 1 - p = 0.50
I'll let you take it from here.
The time it takes for climbers to reach the highest point of a mountain is normally distributed with a standard deviation of 0.75 hours. If a sample of 35 people is drawn randomly from the population, what would be the standard error of the mean of the sample
To find the standard deviation of the number of people who eventually contract the disease, we need to use the concept of a binomial distribution. In this case, the probability of an individual contracting the disease is p = 0.50.
The formula to calculate the standard deviation (σ) of a binomial distribution is:
σ = √(n * p * q),
where n is the number of trials and q is the probability of failure (1 - p).
In this case, we have 1,940 individuals participating in the study, so n = 1,940. Since the probability of contracting the disease is 0.50, the probability of not contracting the disease is q = 1 - 0.50 = 0.50.
Now, let's calculate the standard deviation:
σ = √(1,940 * 0.50 * 0.50)
= √(970 * 0.50)
= √485
≈ 22.05 (rounded to 2 decimal places)
Therefore, the standard deviation of the number of people who eventually contract the disease is approximately 22.05.