The weight of certain population of young females is approximately normally distributed with the mean of 66 kg and a standard deviation of 7.5 kg. If an individual is selected at random from this population, find:

Question

4.1 The probability that she will weigh more than 77.5 kg.

4.2 The percentage of women who will weigh less than 64.5 kg.

Answer 1

To solve these problems, we need to use the normal distribution formula:

z = (x - mean) / standard deviation

4.1
First, calculate the z-score for x = 77.5 kg:

z = (77.5 - 66) / 7.5
z = 1.533333...

Next, we find the probability that she will weigh more than 77.5 kg using a standard normal distribution table or a calculator. The probability for z = 1.53 is approximately 0.0630.

So, the probability that she will weigh more than 77.5 kg is 0.0630 or 6.3%.

4.2
Next, calculate the z-score for x = 64.5 kg:

z = (64.5 - 66) / 7.5
z = -0.2

Find the percentage of women who will weigh less than 64.5 kg using a standard normal distribution table or a calculator. The probability for z = -0.2 is approximately 0.4207.

So, the percentage of women who will weigh less than 64.5 kg is 42.07%.