AP Statistics HW: p95 22

1
AP StatisticsHW p95 22 24, 27 (skip part
c)Obj to understand and use a z-score and
standard normal distribution

• Do Now
• The mean monthly cost of gas is 125 with a
  standard deviation of 10. The distribution of
  the gas bills is approximately normal.
• What percentage of homes have a monthly bill of
  more than 115?
• Less than 115?
• What bill amount represents the top 16 percent?
• What bill amount represents the top 84
• How many standard devations above the mean is a
  bill of 150?
• C2 D4

2
Z-Score (standardized value)

• Allows us to identify the position of a data
  value relative to the µ and s of its set of data
  values.
• z x µ
• s

3

• Ex If x 13.75, µ 10, and s 2.5, then the
• z-score 13.75 10
• 2.5
• This means that 13.75 is 1.5 standard deviations
  above the mean of 10

4

• Ex If x 100, µ 120, and s 15, calculate
  the z-score and tell what it means.

5

• If a variable x, which takes on the values
• x x1, x2, , xn
• has a normal distribution N(µ, s) and we change
  every data value into its standardized score
  (z-score), this new variable z takes on the
  values
• z z1, z2, , zn
• and has the normal distribution N(0, 1) which we
  call the standard normal distribution

6
Standard Normal Distn
7

• Ex A student scores 625 on the math section of
  the SAT and a 28 on the math section of the ACT.
  She can only report one score to her college. If
  the SAT summary statistics include µ 490 and s
  100 and the ACT summary statistics include µ
  21 and s 6, which score should she report?

8

• Ex For data with a distribution N(0,1)
  calculate the following percentages
• of data values between -1 and 1.
• of data values less than 1.
• of data values greater than -1.
• of data values less than 2.
• For what data values are 99.85 of the scores
  lower?
• Do p.95 19, 20