The probability that X₈ is between 495 and 505 pounds is closest to A).0228 B).3174 C).9772 D).6826 E).3830

Question

Quizplus · Accepted Answer

Since the distribution is normal, we can use the formula for z-score:

z = (x - μ) / σ

where x is the weight (500 pounds in this case), μ is the mean weight (500 pounds also) and σ is the standard deviation (10 pounds).

z for 495 pounds:

z = (495 - 500) / 10 = -0.5

z for 505 pounds:

z = (505 - 500) / 10 = 0.5

Using the z-table, we can find the probability for z-values between -0.5 and 0.5.

The area under the curve between -0.5 and 0.5 is 0.6826 or approximately 68.26%.

Therefore, the answer is D) 0.6826.

The Probability That X8 Is Between 495 and 505 Pounds