Question

For a dataset with a mean of 25 and a standard deviation of 3.8, if P(x < k) = 0.45, what is the value of 'k'?

a) 23.22
b) 24.65
c) 26.38
d) 28.11

Answer 1

To find the value of 'k' in the equation P(x < k) = 0.45, use the standard normal distribution table by converting the given probability to a z-score and then finding the corresponding value of 'k'.

Step-by-step explanation:

To find the value of 'k' in the equation P(x < k) = 0.45, we can use the standard normal distribution table. Since we know the mean and standard deviation of the dataset, we can convert the given probability to a z-score, and then use the z-score to find the corresponding value of 'k' from the standard normal distribution table.

First, find the z-score for a probability of 0.45 using the standard normal distribution table. The z-score for a probability of 0.45 is approximately -0.12566.

Next, use the formula z = (x - mean) / standard deviation to find the value of 'k'. Rearranging the formula, we get x = z * standard deviation + mean. Plugging in the known values, we get x = -0.12566 * 3.8 + 25 = 24.5244. Rounded to two decimal places, the value of 'k' is 24.52.