Answer :
Final answer:
To calculate the mean number of individuals with a genetic mutation in a sample of 114 people, where the prevalence of the mutation is 7%, we multiply the sample size (114) by the probability (0.07), which gives a mean of 7.98, or approximately 8 individuals. The answer is option C.
Explanation:
The question deals with probability and statistics, specifically the concept related to expected values in a population sample. Given that 7% of the population has a particular genetic mutation, we want to find the mean number of people with this mutation in a group of 114 randomly selected individuals.
To find this mean, we use the formula for the expected value of a binomial distribution:
Mean = n * p
where:
- n is the size of the sample (114 people)
- p is the probability of finding an individual with the genetic mutation (7%, or 0.07)
Calculation:
Mean = 114 * 0.07 = 7.98
Therefore, the mean number of people with the genetic mutation in such groups of 114 is approximately 8 (Option c).
