NORMAL DISTRIBUTION 1) The heights of students at a local university are normally distributed with a mean of 168cm and a standard deviation of 8cm. One of these students is chosen at random. a) Find the probability that the height of the student is: i) less than 172cm ii) between 160cm and 170cm b) Given that 30% of all these students have heights less than Hcm, find the value of H, correct to one decimal place.

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NORMAL DISTRIBUTION
1) The heights of students at a local university are normally distributed with a mean of
168cm and a standard deviation of 8cm. One of these students is chosen at random.
a) Find the probability that the height of the student is:
i) less than 172cm
ii) between 160cm and 170cm
b) Given that 30% of all these students have heights less than Hcm, find the value of
H, correct to one decimal place.
2) The speeds of vehicles passing a point on the roadside of a highway are normally
distributed with a mean of 102 km/h and a standard deviation of 15 km/h.
a) Find the probability that the speed of a vehicle, selected at random:
i) is less than 75 km/h
ii) lies between 78 km/h and 114 km/h
b) The number of vehicles passing in one hour is 245. Estimate the number of those
which exceeds the speed limit of 120 km/h.
Transcribed Image Text:NORMAL DISTRIBUTION 1) The heights of students at a local university are normally distributed with a mean of 168cm and a standard deviation of 8cm. One of these students is chosen at random. a) Find the probability that the height of the student is: i) less than 172cm ii) between 160cm and 170cm b) Given that 30% of all these students have heights less than Hcm, find the value of H, correct to one decimal place. 2) The speeds of vehicles passing a point on the roadside of a highway are normally distributed with a mean of 102 km/h and a standard deviation of 15 km/h. a) Find the probability that the speed of a vehicle, selected at random: i) is less than 75 km/h ii) lies between 78 km/h and 114 km/h b) The number of vehicles passing in one hour is 245. Estimate the number of those which exceeds the speed limit of 120 km/h.
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