To solve this problem, we need to use the concept of Z-scores in statistics. The Z-score is a measure of how many standard deviations an element is from the mean.

Step 1: Calculate the Z-scores for 55kg and 60kg.

The formula for a Z-score is Z = (X - μ) / σ, where X is the value we're interested in, μ is the mean, and σ is the standard deviation.

For 55kg: Z1 = (55 - 62) / 5 = -1.4
For 60kg: Z2 = (60 - 62) / 5 = -0.4

Step 2: Look up these Z-scores in a standard normal distribution table, or use a calculator that can do this for you.

The values you get from the table are the probabilities that a value is less than your given value.

For Z1 = -1.4, the probability P(Z

Question

To solve this problem, we need to use the concept of Z-scores in statistics. The Z-score is a measure of how many standard deviations an element is from the mean.

Step 1: Calculate the Z-scores for 55kg and 60kg.

The formula for a Z-score is Z = (X - μ) / σ, where X is the value we're interested in, μ is the mean, and σ is the standard deviation.

For 55kg: Z1 = (55 - 62) / 5 = -1.4
For 60kg: Z2 = (60 - 62) / 5 = -0.4

Step 2: Look up these Z-scores in a standard normal distribution table, or use a calculator that can do this for you.

The values you get from the table are the probabilities that a value is less than your given value.

For Z1 = -1.4, the probability P(Z < -1.4) = 0.0808
For Z2 = -0.4, the probability P(Z < -0.4) = 0.3446

Step 3: Subtract the two probabilities to get the probability that a student weighs between 55kg and 60kg.

P(55kg < X < 60kg) = P(Z < -0.4) - P(Z < -1.4) = 0.3446 - 0.0808 = 0.2638

So, the probability that a randomly selected student weighs between 55 and 60kg is 0.2638 or 26.38%. Therefore, the correct answer is c. 0.2638.

Knowee AI · Accepted Answer