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Statistics
5.1-5.3 Group Quiz
1. X is a random variable with a normal distribution and a mean value of 6 and a standard
deviation of 2. Convert the following x-values into their corresponding z-scores. Round to
2 decimal places.
a) x = 4
b) x = 8
c) x = 10.75
2. x is a random variable with a normal distribution and a mean value of 6 and a standard
deviation of 2. Find the following probabilities. Leave the 4-digit value from the table.
a) P( x  4)
b) P ( x  10.75)
c) P (4  x  8)
3. The distribution of weights for children of a given age and gender is approximately
normal. This fact allows a doctor or nurse to find from a child’s weight the weight
percentile of the population to which the child belongs. Typically, this is done using special
charts provided to medical personnel, but these percentiles can also be computed using
facts about approximately normal distributions.
a) The distribution of weights for 6-month old baby boys is approximately normal with
  17.50 pounds and   2 pounds. What percentage of 6-month old baby boys weigh
more than 19 pounds? Round your answer to two decimal places.
b) The distribution of weights for 6-month old baby boys is approximately normal with
  17.50 pounds and   2 pounds. What percentage of 6-month old baby boys weigh
less than 16 pounds? Round your answer to two decimal places.
c) What weight would put a 6-month old baby boy in the top 30% of all weights?
4. In 1998, 1,172,779 college-bound seniors took the SAT exam. The distribution of
scores in the math section of the SAT was approximately normal with a mean score of 512
and a standard deviation of 112.
a) Suppose a student scored in the 95th percentile. What test score would this correspond
to?
b) A certain university only accepts applicants who scored in the top 25% of all SAT scores
that year. What would the cut-off score be to be accepted into this university?
c) How many of the 1,172,779 college-bound seniors scored less than 600? Round your
answer to the nearest whole number.