**1)** Simulate flipping a fair coin by performing the following operations.

a) Randomly generate a column of data (c1) with 1750 entries { Calc\Random Data\Integer }. Minimum number is 0 and maximum number is 1.

b) Randomly generate a column of data (c2) with 3500 entries { Calc\Random Data\Integer }. Minimum number is 0 and maximum number is 1.

c) Randomly generate a column of data (c3) with 9500 entries { Calc\Random Data\Integer }. Minimum number is 0 and maximum number is 1.

d) Find the empirical probabilities for c1, c2, and c3 { Stat\Tables\Tally Individual Variables }. Be sure to check both counts (Frequency) and percents (relative frequency).

e) In which sample did the empirical probabilities, most closely match the theoretical probability of 0.5 ? Why ?

**2)** If you roll a pair of dice, the probability distribution for the sum of the face value of the dice is given in the following table.

a) Use MINITAB to simulate rolling a pair of dice 9000 times.

i) Randomly generate two columns { C1 and C2 } from the appropriate discrete distribution { Calc\Random Data\ Integer }. Minimum 1 and Maximum 6. C1 represents roll on first die and C2 represents roll on second die.

ii) Add C1 and C2 and place the results in C3 { Calc\Row Statistics } C3 represents the sum of the dice.

b) Find the empirical mean and empirical standard deviation for the sum of the pair of dice {C3}. { Stat\Basic Statistics\Display Descriptive Statistics }

c) Compare the empirical results in part (b) to the theoretical values of µ & σ

For Problems # 3 and 4.

Probability finds P(X = x)

Cumulative Probability finds P(X ≤ x)

Inverse Cumulative Probability finds P(X ≤ x0 )= value

**3)** Let X~Uniform(6,32). Use MINITAB OUTPUT to find each of the following. { Calc\Probability Distributions\Uniform }

Choose input constant to enter the correct X value on each question.

a) P(X < 23)

b) P(X ≥ 18)

c) P(16< X < 30)

d) Xo when P(X < Xo) = 0.61

e) Xo when P(X > Xo) = 0.42

**4)** Let X~Normal(µ =40, σ²=49). Use MINITAB OUTPUT to find each of the following. { Calc\Probability Distributions\Normal }

Choose input constant to enter the correct X value on each question.

a) P(X < 38)

b) P(X ≥ 45)

c) P(38 < X < 62)

d) Xo when P(X < Xo) = 0.70

e) Xo when P(X > Xo) = 0.38

**5)** The following data set represents the repair costs (in dollars) for a random sample of 24 dishwashers. { Note: the data listed below should be entered into one column.}

41.82 | 52.81 | 78.16 | 83.48 | 78.88 | 88.13 | 88.79 | 90.07 | 90.35 | 91.72 |

95.43 | 96.50 | 101.32 | 105.59 | 105.62 | 111.32 | 117.14 | 118.42 | 118.77 | 119.01 |

130.70 | 141.52 | 141.84 | 147.06 |

Use MINITAB to construct a 88% confidence interval for the population mean.

{ Stat/Basic Statistics/1-sample t }

**6)** In MINITAB generate 100 columns of data with 100 observations in each column from a Normal distribution with { Calc\Random Data\Normal }. Find an appropriate 92% confidence interval for the population mean using each of the 100 samples. { Stat/Basic Statistics/1-sample z }

a) What are the 100 confidence intervals (MINITAB output)?

b) How many of these intervals are expected to contain the mean of the population?

c) Based on your Minitab output, how many of these intervals actually contain the mean of the population ()?

**7)** A credit card company thinks that the mean value of the purchases of card holders in a month has increased from last years average of $225. A random sample of 20 customers monthly purchases was taken and the data is given below. Assume the sample comes from a normal distribution. {Note: the data listed below should be entered into one column.}

207.65 | 240.05 | 278.89 | 298.66 | 256.27 | 195.70 | 187.65 | 300.42 | 288.95 | 296.75 |

210.15 | 216.16 | 286.72 | 297.40 | 226.70 | 235.90 | 140.65 | 202.66 | 250.50 | 365.78 |

(a) Obtain the MINITAB output needed to conduct the appropriate test of hypothesis to determine if the mean value of the purchases has increased from last year. { Stat/Basic Statistics/1-Sample t }

(b) Using the P-value obtained in the MINITAB output, what is your conclusion using a 0.01 level of significance.

conclusion using a 0.01 level of significance.

level of significance.

**8)** Enter the following data set into two columns in the data window. Keeping the order pairs across from each other. A study was performed on the wear of a bearing, y, and the relationship to oil viscosity, x. The following data were obtained :

a) Calculate the linear regression information. { Stat\Regression\Regression }

b) Write the linear correlation coefficient and interpret it.

c) Write the coefficient of determination and interpret it.

d) Write the line of best fit or regression equation.

e) Use the regression equation to predict the wear of a bearing or explain why not if oil viscosity is 122.

f) Use the regression equation to predict the wear of a bearing or explain why not if oil viscosity is 25.

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