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STAT THIRD QUARTER EXAM REVIEWER #3

Quiz by JONALD ROSARIO

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13 questions
Show answers
  • Q1
    Which of the following is a defining feature of a normal distribution?
    It is always skewed.
    It has a symmetric, bell-shaped curve.
    It consists only of whole numbers.
    It has a uniform shape.
    30s
  • Q2
    Fill in the blanks with the correct percentages of data contained within one, two, and three standard deviations of the mean in a normal distribution: ___%, ___%, ___%.
    68%, 95%, 99.7%
    50%, 90%, 98%
    60%, 80%, 90%
    75%, 85%, 95%
    30s
  • Q3
    TRUE or FALSE: In a standard normal distribution, the area to the right of z = 0 is 50%.
    It depends on the mean.
    It depends on the standard deviation.
    TRUE
    FALSE
    30s
  • Q4
    Given a normal random variable X with mean μ = 100 and standard deviation σ = 20, convert X = 120 to its equivalent standard normal variable Z.
    Z = 0
    Z = 1
    Z = 0.5
    Z = 2
    30s
  • Q5
    Calculate the Z-scores for the following values: X = 90, 110, and 130, given μ = 100 and σ = 10.
    Z = -1, 1, 2
    Z = 1, 2, 3
    Z = 0, 1, 2
    Z = -1, 1, 3
    30s
  • Q6
    The company plans to improve quality by reducing the standard deviation from 40 hours to 25 hours. How does this change affect the probability of batteries lasting between 560 and 640 hours?
    The probability increases because the distribution becomes more concentrated around the mean.
    The probability decreases because the z-scores for the range narrow.
    The probability increases because the z-scores for the range widen.
    The probability remains unchanged because the mean is the same.
    30s
  • Q7
    Which of the following is a characteristic of a normal random variable?
    It consists only of negative values.
    It has a skewed distribution.
    It has a bell-shaped curve.
    It is always discrete.
    30s
  • Q8
    List the percentages of data contained within one, two, and three standard deviations from the mean in a normal distribution. Fill in the blanks: ____%, ____%, ____%.
    65%, 93%, 99%
    68%, 95%, 99.7%
    70%, 90%, 98%
    75%, 85%, 95%
    30s
  • Q9
    TRUE or FALSE. The region under the normal curve to the left of z=0 corresponds to 50% of the total area. Answer: ________
    TRUE
    MAYBE
    FALSE
    NOT SURE
    30s
  • Q10
    Given a normal random variable X with μ=50 and σ=10, convert X=60 to its equivalent standard normal variable Z. Answer: ________
    1
    2
    -1
    0
    30s
  • Q11
    Calculate the Z-scores for the following values of X = 45, 55, and 65, given μ = 50 and σ = 5. Answers: _________, __________, __________.
    0, 1, 2
    -1, 1, 4
    -1, 1, 3
    -1, 0, 3
    30s
  • Q12
    The company wants to improve the quality of its bulbs by reducing the standard deviation from 50 hours to 30 hours. Analyze how this change affects the probability of bulbs lasting between 750 and 850 hours.
    The probability decreases because the z-scores for the range narrow.
    The probability remains unchanged because the mean lifespan is unaffected.
    The probability increases because the z-scores for the range widen.
    The probability increases because the distribution becomes narrower around the mean.
    30s
  • Q13
    How does decreasing the standard deviation of a product's lifespan from 40 hours to 25 hours affect the probability of the product lasting within a specified range?
    The probability increases because the z-scores for the range become larger.
    The probability remains the same because the mean lifespan does not change.
    The probability decreases because the spread of the distribution widens.
    The probability increases because the distribution becomes more concentrated around the mean.
    30s

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