Question 11 Batches of a chemical contain random amounts of lead with a mean value of 6.0 mg and a standard deviation of 2.0 mg. If 50 batches are prepared, the probability that their average amount of lead is greater than 6.5 mg is:

0.0384

Step-by-step explanation:

Given that:

Mean (m) = 6.0

Standard deviation (s) = 2.0

Sample size (n) = 50

Probability that average amount is greater than 6.5

P(x > 6.5)

Obtain the Zscore using the relation :

Zscore = (x - m) / (s / sqrt(n))

Zscore = (6.5 - 6.0) / (2 / sqrt(50))

Zscore = 0.5 / 0.2828427

Zscore = 1.7677

Zscore = 1.77

P(Z > 1.77) = 1 - P(Z < 1.77)

P(Z > 1.77) = 1 - 0.9616

P(Z > 1.77) = 0.0384