Dallas Green Homes uses a normal curve to estimate next year's demand.The distribution has a mean of 163 units and a standard deviation of 36 units.According to this demand distribution.If demand exceeds 95 units, the company will have to expand.How likely is it that expansion will be necessary?
A).9429
B).9706
C).9131
D).9878
E).8980

Question

Quizplus · Accepted Answer

To find the likelihood that demand exceeds 95 units, we calculate the Z-score for 95 units using the formula Z = (X - μ) / σ, where X is the value in question (95 units), μ is the mean (163 units), and σ is the standard deviation (36 units). The Z-score is (95 - 163) / 36 = -68 / 36 = -1.89. Looking up the Z-score of -1.89 in a standard normal distribution table or using a calculator, we find that the area to the left of this Z-score is approximately 0.0294. Since we're interested in the probability of demand exceeding 95 units, we subtract this value from 1 (1 - 0.0294 = 0.9706), indicating a 97.06% likelihood that expansion will be necessary.

Dallas Green Homes Uses a Normal Curve to Estimate Next