the amount of pollutants that are found in waterways near large cities is normally distributed with a mean of 9.1 ppm and a standard deviation of 1.5 ppm. 9 randomly selected large cities are studies. for the 9 cities, find the probability that the average amount of pollutants is less than 9.6 ppm.?

Step-by-step explanation:

Let x be the random variable representing the amount of pollutants that are found in waterways near large cities. Since it is normally distributed and the population mean and population standard deviation are known, we would apply the formula,

z = (x - µ) / (σ/√n)

Where

x = sample mean

µ = population mean

σ = standard deviation

n = number of samples

From the information given,

µ = 9.1

σ = 1.5

n = 9

the probability that the average amount of pollutants is less than 9.6 ppm is expressed as

P (x < 9.6)

z = (9.6 - 9.1) / (1.5/√9) = 1

Looking at the normal distribution table, the probability corresponding to the z score is 0.84

Therefore,

P (x < 9.6) = 0.84