North Pacific Cannery (NPC) in British Columbia cans an average of 1250 cases of salmon daily, with a standard deviation of 40 cases.Assuming output has a normal distribution, on what proportion of days is NPC's output either less than 1180 cases or more than 1320 cases?
A).0802
B).1082
C).1193
D).0925
E).1367

Question

Quizplus · Accepted Answer

To find the proportion of days NPC's output is either less than 1180 cases or more than 1320 cases, we calculate the Z-scores for both values and use the standard normal distribution. For 1180 cases: $Z = \frac{1180 - 1250}{40} = -\frac{70}{40} = -1.75$For 1320 cases: $Z = \frac{1320 - 1250}{40} = \frac{70}{40} = 1.75$Using standard normal distribution tables or a calculator, the area to the left of $Z = -1.75$ is approximately 0.0401, and the area to the right of $Z = 1.75$ is also approximately 0.0401. To find the total proportion of days, we add these two areas: $0.0401 + 0.0401 = 0.0802$. Therefore, on approximately 8.02% of the days, NPC's output is either less than 1180 cases or more than 1320 cases.

North Pacific Cannery (NPC) in British Columbia Cans an Average