Download Stats Assignment

STATISTICS ASSIGNMENT
1. Determine the mean, median and the mode for the following
1, 2, 3, 4, 4, 7
2. Find the mean, mode and the standard deviation for the following frequency
distribution showing student IQ (picture yourself at the bottom!):
3. Find the mean and standard deviation for the following graph:
4. What do each of the following signify?
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Small standard deviation
Large standard deviation
Standard deviation of zero
5. If Z is a random variable with a standard normal distribution:
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determine P(-0.62<Z<0.75)
if P(Z<a) = 0.8 determine “a”.
6. If X is a random variable with normal distribution
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determine P(-3X9), if   4 and   10
if P(Xb)=0.6 and   4 and   10 determine “b”.
7. The attendance for a week at the local theatre is normally distributed with a
mean of 4 000 and a standard deviation of 500. What percentage of attendance
figures fall between 3 600 and 4 600 people?
8. A provincial Math exam has a mean of 68 and a standard deviation of 13.2. If 30
000 students take the exam and a score of 49 or less fail, how many students fail
the exam?
9. A normal random variable X has a mean of 80. If the probability that X is less
than 72 is 15%, what is the standard deviation of X?
10. A test to a large group of students approximates the normal curve. The mean is
70 with a standard deviation of 8. If 8% of the students receive A’s and 16%
receive B’s, what is the minimum mark needed to receive a B?
11. A fair die is rolled 100 times. Use a normal approximation to calculate the
probability of rolling:
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20 fours
at most 20 fours
less than 20 fours
between 15 and 22 fives, exclusive
between 15 and 22 fives, inclusive
12. If the failure rate for first-year calculus students in university is 40%, find the
probability that 8 or fewer students in a class of 30 will fail.
13. A baseball player’s batting average is .300; find the probability of getting 25 or
more hits in the next 100 times at bat.
14. The probability that a tire manufactured will be defective is 4%. With 180 tires,
what is the probability that no more than 6 are defective?
15. Find the mean and standard deviation for: a – 2b, a, a + 2b