Question

A scientist studying water quality measures the lead level in parts per billion (ppb) at each of 49 randomly chosen locations along a water line. Suppose that the lead levels across all the locations on this line are strongly skewed to the right with a mean of ppb17 and a standard deviation of 14ppb. Assume that the measurements in the sample are independent.

Required:
What is the probability that the mean lead level from the sample of 49 measurements T is less than 15 ppb?

Answer 1

0.16

Explanation:

Answer 2

The probability that the mean lead level from the sample of 49 measurements T is less than 15 ppb

P(x⁻< 15) = 0.1587

Explanation:

Step(i):-

Given that the size of the sample 'n' =49

Mean of the Population = 17ppb

The standard deviation of the population = 14ppb

Let 'X' be the random variable in a normal distribution

`Z = (x-mean)/((S.D)/(√(n) ) ) = (15-17)/((14)/(√(49) ) ) = -1`

Step(ii):-

The probability that the mean lead level from the sample of 49 measurements T is less than 15 ppb

P(x⁻< 15) = P(Z<-1) = 1-P(Z>-1)

= 1-(0.5+A(-1))

= 0.5 - A(1)

= 0.5-0.3413

= 0.1587

Final answer:-

The probability that the mean lead level from the sample of 49 measurements T is less than 15 ppb

P(x⁻< 15) = 0.1587