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.

Question

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.

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

Answer 1

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.