In this problem, we have a variable normally distributed X such that:
• X = average of mosquitos per square meter,
,
• the mean ,μ = 60 mosquitos/m²,,
,
• the standard deviation ,σ = 16 mosquitos/m²,.
We want to compute the probability that the average of mosquitos will be:
Now, we can rewrite this probability in the following way:
Because the variable is normally distributed, we can compute the probability using the z-scores:
The probability in terms of the z-score is:
Where we have used a table to get the value of z-score probability P(Z ≤ 0.18).
Answer
The probability that the average of those counts is more than 62.9 mosquitos/m² is 0.4281.