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:
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.
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%.