Question

Sixth grade boys' average weight is 100 pounds with a standard deviation of 8 pounds. What is the probability that a randomly selected 6th grade boy weighs less than 116 pounds?

about 97.5%
about 90%
about 95%
about 99%

Answer 1

Answer : D is correct

Given: Sixth grade boys' average weight is 100 pounds with a standard deviation of 8 pounds.

Explanation: The probability that a randomly selected 6th grade boy weighs less than 116 pounds can be calculated as follows:

Step 1: Find the z-scoreTo find the z-score, use the formula: z = (x - μ) / σwhere x = 116, μ = 100, and σ = 8z = (116 - 100) / 8z = 2.0

Step 2: Find the probabilityUsing a z-table or calculator, we can find the probability that a z-score is less than 2.0.

The probability is approximately 0.9772 or about 97.72%.

Therefore, the probability that a randomly selected 6th grade boy weighs less than 116 pounds is about 97.72%.

Round it to the nearest whole number to get the answer which is about 98%.

Thus, option D is correct.

Answer 2

The probability that a randomly selected 6th grade boy weighs less than 116 pounds is about 97.5%.Explanation:Given: Average weight of sixth-grade boys= 100 poundsStandard deviation= 8 poundsWe have to find: Probability that a randomly selected 6th grade boy weighs less than 116 pounds.Z-score is given by the formula:(Value - Mean) / Standard DeviationLet x be the weight of the sixth-grade boy.The z-score will be given as:z = (x - μ) / σwhere μ is the mean weight, σ is the standard deviation.Now we can find the probability using a z-table.The z-table shows the probability that a standard normal distribution will be less than a certain value. Since we can't use the table directly to find the probability less than a particular value, we must convert x into a z-score before using the table.The Z score is calculated as shown below.z = (x - μ) / σ= (116 - 100) / 8= 2.00Using the z-table, we can find that the probability of a z-score less than 2.00 is about 0.975 or 97.5%.Hence, the probability that a randomly selected 6th grade boy weighs less than 116 pounds is about 97.5%.Therefore, option A is correct.