luxury passenger liner has 500 passengers on board whose ages are normally distributed around a mean of 60 years with a standard deviation of 12 years./ ’n Luukse passasierskip het 500 passasiers aan boord. Hul ouderdomme word normal verdeel om ‘n gemiddelde van 60 jaar heen, met ‘n standaardafwyking van 12 jaar.

2.2​What percentage of the passengers is between 48 and 72 years old? Watter persentasie van die passasiers is tussen 48 en 72 jaar oud?

1 answer

To find the percentage of passengers between 48 and 72 years old, we need to first find the z-scores for these ages and then use the standard normal distribution table.

For 48 years old:
z = (48 - 60) / 12 = -1

For 72 years old:
z = (72 - 60) / 12 = 1

Using the standard normal distribution table, we can find the probability of being between these z-scores:
P(-1 < Z < 1) = P(Z < 1) - P(Z < -1)
= 0.8413 - 0.1587
= 0.6826

Therefore, approximately 68.26% of the passengers on board are between 48 and 72 years old. Dit beteken dat ongeveer 68.26% van die passasiers aan boord tussen 48 en 72 jaar oud is.