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:
4.1The probability that she will weigh more than 77.5 kg. / Die waarskynlikheid dat sy meer as 77.5 kg sal weeg.
To find the probability that she will weigh more than 77.5 kg, we first need to calculate the z-score for this value using the formula:
z = (x - μ) / σ
where x is the weight of 77.5 kg, μ is the mean weight of 66 kg, and σ is the standard deviation of 7.5 kg.
z = (77.5 - 66) / 7.5 = 1.5
Next, we look up the corresponding z-score of 1.5 in the standard normal distribution table or use a calculator to find that the probability of a z-score greater than 1.5 is approximately 0.0668.
Therefore, the probability that she will weigh more than 77.5 kg is approximately 0.0668 or 6.68%.