An IQ score is one way of measuring a person's intelligence, with an IQ score of 100 being considered as average for the general population. The distribution of IQ scores for the inmates of a certain prison is found to follow a normal distribution with a mean of 95 and a standard deviation of 10. Any prisoner found to have an IQ of less than 70 is considered to have special needs and must be relocated to a special section of the prison.
(a) What percentage (to 2 decimal places) of inmates are considered to have an IQ equal to or above the average for the general population?
(b) What percentage (to 2 decimal places) of inmates could be classified as having special needs?
(c) What percentage (to 2 decimal places) of inmates would be classified as having an IQ less than the average for the general population but not with special needs?
(d) 10 new inmates arrive in the prison. Assuming their IQ scores follow the same distribution as above. What is probability that at least one inmate will need to be relocated because of their special needs?
(e) One of the inmates is tested and found to have an IQ less than the average for the general population. What is the probability that they have special needs?
(f) In a prison containing 1000 inmates how many would you expect to be located in the special needs section.
(a) What percentage (to 2 decimal places) of inmates are considered to have an IQ equal to or above the average for the general population?
(b) What percentage (to 2 decimal places) of inmates could be classified as having special needs?
(c) What percentage (to 2 decimal places) of inmates would be classified as having an IQ less than the average for the general population but not with special needs?
(d) 10 new inmates arrive in the prison. Assuming their IQ scores follow the same distribution as above. What is probability that at least one inmate will need to be relocated because of their special needs?
(e) One of the inmates is tested and found to have an IQ less than the average for the general population. What is the probability that they have special needs?
(f) In a prison containing 1000 inmates how many would you expect to be located in the special needs section.
