Complete the following:
Q1: We know the IQ of people is normally distributed with mean 120 and standard deviation (SD) of 25. Calculate the probability that an adult will have
a ) IQ less than 100
b) IQ greater than 150
c) IQ between 100 and 150
d) Any person with a score over 200 is considered a genius. In a population of 10000 how many will score above 200.
e) MENSA is a set up to recruit the top 1% of the population. What should the IQ score be set at to qualify for MENSA membership?
Q2: A chemical company produces a product which has an impurity that is expensive to remove. The mean level is 20 parts per million with SD of 6 parts.
a) What level of impurity could the chemical company quote to its customers and be 99% confident that it will not exceed the stated impurity level?
A customer, however, is only prepared to accept a maximum impurity of 30 parts.
b) How much product will meet this specification?
c) Suppose the product deteriorates so that the mean drifts out to 25 parts per million, but with the same SD of 6 parts. How much of production is now unsuitable?
d) Finally, if the mean is brought back to 20 parts but the SD is the found to be 8 parts, how much product will not meet the specification?
Q3: During tests on a group of workers it is found that only 15% of them can hear sound above a frequency of 200 units and only 6% can detect sound above 210 units. Calculate the mean and SD of the highest frequency that can be heard for the population of workers.