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: / Die gewig van sekere bevolking van jongvrou eis gewoonlik benaderd normaalverdeel met die gemiddelde van 66 kg en 'n standaardafwyking van 7.5 kg. As 'n individu ewekansig gekies word uit hierdie bevolking, vind:
4.2The percentage of women who will weigh less than 64.5 kg. / Die persentasie van die vroue wat minder as 64.5 kg sal weeg.
To find the percentage of women who will weigh less than 64.5 kg, we need to find the z-score corresponding to 64.5 kg and then find the percentage of data that falls below this z-score.
First, we calculate the z-score:
z = (X - μ) / σ
z = (64.5 - 66) / 7.5
z = -1.5 / 7.5
z = -0.2
Next, we look up the z-score of -0.2 in the standard normal distribution table or use a calculator to find that the percentage of data below this z-score is approximately 0.4207 or 42.07%.
Therefore, approximately 42.07% of women in this population will weigh less than 64.5 kg.