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Statistics LibreTexts

7.12: Chapter 7 Solution (Practice + Homework)

  • Page ID
    6058
  • 1.

    1. \(U(24, 26), 25, 0.5774\)
    2. \(N(25, 0.0577)\)
    3. \(0.0416\)

    3.

    0.0003

    5.

    25.07

    7.

    1. \(N(2,500, 5.7735)\)
    2. \(0\)

    9.

    2,507.40

    11.

    1. \(10\)
    2. \(\frac{1}{10}\)

    13.

    \(N(10, \frac{10}{8}))\)

    15.

    0.7799

    17.

    1.69

    19.

    0.0072

    21.

    391.54

    23.

    405.51

    25.

    Mean = 25, standard deviation = 2/7

    26.

    Mean = 48, standard deviation = 5/6

    27.

    Mean = 90, standard deviation = 3/4

    28.

    Mean = 120, standard deviation = 0.38

    29.

    Mean = 17, standard deviation = 0.17

    30.

    Expected value = 17, standard deviation = 0.05

    31.

    Expected value = 38, standard deviation = 0.43

    32.

    Expected value = 14, standard deviation = 0.65

    33.

    0.23

    34.

    0.060

    35.

    1/5

    36.

    0.063

    37.

    1/3

    38.

    0.056

    39.

    1/10

    40.

    0.042

    41.

    0.999

    42.

    0.901

    43.

    0.301

    44.

    0.832

    45.

    0.483

    46.

    0.500

    47.

    0.502

    48.

    0.519

    49.

    1. \(Χ\) = amount of change students carry
    2. \(Χ \sim E(0.88, 0.88)\)
    3. \(\overline X\) = average amount of change carried by a sample of 25 students.
    4. \(\overline X \sim N(0.88, 0.176)\)
    5. \(0.0819\)
    6. \(0.1882\)
    7. The distributions are different. Part 1 is exponential and part 2 is normal.

    51.

    1. length of time for an individual to complete \(IRS\) form 1040, in hours.
    2. mean length of time for a sample of 36 taxpayers to complete \(IRS\) form 1040, in hours.
    3. \(N(10.53, \frac{1}{3})\)
    4. Yes. I would be surprised, because the probability is almost 0.
    5. No. I would not be totally surprised because the probability is 0.2312

    53.

    1. the length of a song, in minutes, in the collection
    2. \(U(2, 3.5)\)
    3. the average length, in minutes, of the songs from a sample of five albums from the collection
    4. \(N(2.75, 0.066)\)
    5. 2.74 minutes
    6. 0.03 minutes

    55.

    1. True. The mean of a sampling distribution of the means is approximately the mean of the data distribution.
    2. True. According to the Central Limit Theorem, the larger the sample, the closer the sampling distribution of the means becomes normal.
    3. The standard deviation of the sampling distribution of the means will decrease making it approximately the same as the standard deviation of X as the sample size increases.

    57.

    1. \(X\) = the yearly income of someone in a third world country
    2. the average salary from samples of 1,000 residents of a third world country
    3. \(\overline X \sim N\left(2000, \frac{8000}{\sqrt{1000}}\right)\)
    4. Very wide differences in data values can have averages smaller than standard deviations.
    5. The distribution of the sample mean will have higher probabilities closer to the population mean.
      \(P(2000 < \overline X < 2100) = 0.1537 \)
      \(P(2100 < \overline X < 2200) = 0.1317\)

    59.

    b

    60.

    64

    61.

    1. Yes
    2. Yes
    3. Yes
    4. 0.6

    62.

    400

    63.

    2.5

    64.

    25

    65.

    0.0087

    66.

    0.0064, 0.0064

    67.

    1. It has no effect.
    2. It is divided by \(\sqrt(2)\).
    3. It is divided by 2.

    68.

    1. 4/5
    2. 0.04
    3. 0.0016

    69.

    1. Yes
    2. No

    70.

    0.955

    71.

    0.927

    72.

    0.648

    73.

    0.101

    74.

    0.273