Session packet
Statistics 226
Supplemental Instruction
Iowa State University / Leader: / Luyun
Course: / Stat 226
Instructor: / Anna Peterson
Date: / 2/9/16

Here were our steps when given a value or values and asked to find a percent:

  1. Use the problem to sketch a graph of the normal distribution involved
  2. Calculate the appropriate deviation using the value(s) and the mean (using subtraction)
  3. Find the corresponding z-score by dividing thedeviation by the standard deviation
  4. Find an approximation of this z-score using the row and column titles on the z-table
  5. Findthe corresponding percent in the body of the z-table
  6. Label the desired percent on the graph
  7. Revisit the graph and the problem to apply and adjust your percent to answer the question

Here were our steps when given a percent and asked to find values:

  1. Use the problem to sketch a graph of the normal distribution involved
  2. Find the desired percent on the graph
  3. Find an approximation of this percent in the body of the z-table
  4. Find the corresponding z-score using the row and column titles on the z-table
  5. Find the corresponding deviation by multiplying the z score by the standard deviation
  6. Calculate the appropriate value(s) using the deviation and the mean (using addition or subtraction)
  7. Revisit the graph and the problem to apply and adjust your value(s) to answer the question

Multiple choice

  1. On the basis of chance, the probability of obtaining a value which falls between z = .50 and z = l.00 under the standard normal curve is approximately:
    a. 5 in a hundred
    b. 34 in a hundred
    c. l5 in a hundred
    d. 20 in a hundred
  1. What proportion of cases in a normally distributed population will have z-scores greater than l.0 or less than -l.0?
    a. .l0
    b. 0.32
    c. 0.50
    d. 0.68
  1. Given a normal distribution with a mean of 80 and a standard deviation of 5, we know that approximately what percent of the values are between 70 and 90?
    a. 68
    b. 95
    c. 99
    d. 99.7
  1. What is the probability that a value picked at random from the standard normal distribution will be between -1.96 and 1.96?
    a. 0.997
    b. 0.90
    c. 0.68
    d. 0.95
  1. The test scores of 600 students are normally distributed with a mean of 76 and a standard deviation of 8. The number of students scoring 90 and above is:
    a. 175
    b. 24
    c. 276
    d. 576

Ture or false

  1. The area under any normal curve is equal to 1.
  2. In order to compute probabilities associated with a non-standard normal distribution, one must first convert to the standard normal distribution.
  3. Normal distributions are discrete distributions.
  4. As the standard deviation of a normal distribution increases, the height of the normal curve increases.
  5. The probability that the value of a normal random variable falls within one standard deviation of the mean is .5.
  6. P(Z > 2.3) = P(Z < -2.3)
  1. Amongallthecomputerchipsproducedbyacertainfactory,6percentaredefective.A sample of 400 chips is selected forinspection.

(a)Whatistheprobabilitythatthissamplecontainsbetween20and25defectivechips(including 20 and25)?

(b)Suppose that each of 40 inspectors collects a sample of 400 chips. What is theprobabilitythatatleast8inspectorswillfindbetween20and25defectivechipsintheirsamples?

  1. The BMI for males age 20 to 74 is follows approximately a normal distribution with mean μ = 27.9 and standard deviation σ = 7.8. Use the 68-95-99.7 rule to find

1) The percentage of males with BMI less than 20.1.

2) The percentage of males with BMI greater than 12.3.

3) The BMI values that correspond to the middle 99.7% of the distribution.

4) The value such that 0.15% of males have BMI’s greater than the value.

  1. The annual salaries of employees in a large company are approximately normally distributed with a mean of $50,000 and a standard deviation of $20,000.
    a) What percent of people earn less than $40,000?

b) What percent of people earn between $45,000 and $65,000?

c) What percent of people earn more than $70,000?