# mat540 - Quiz - Week- 2

Seventy two percent of all observations fall within 1 standard deviation of the mean if the data is normally distributed.

If two events are not mutually exclusive, then P(A or B) = P(A) + P(B).

Probability trees are used only to compute conditional probabilities.

The minimin criterion is optimistic.

Using the minimax regret criterion, we first construct a table of regrets. Subsequently, for each possible decision, we look across the states of nature and make a note of the maximum regret possible for that decision. We then pick the decision with the largest maximum regret.

Both maximin and minimin criteria are optimistic.

The equal likelihood criterion assigns a probability of 0.5 to each state of nature, regardless of how many states of nature there are.

Assume that it takes a college student an average of 5 minutes to find a parking spot in the main parking lot. Assume also that this time is normally distributed with a standard deviation of 2 minutes. Find the probability that a randomly selected college student will take between 2 and 6 minutes to find a parking spot in the main parking lot.

The chi-square test is a statistical test to see if an observed data fit a _________.

The metropolitan airport commission is considering the establishment of limitations on noise pollution around a local airport. At the present time, the noise level per jet takeoff in one neighborhood near the airport is approximately normally distributed with a mean of 100 decibels and a standard deviation of 3 decibels. What is the probability that a randomly selected jet will generate a noise level of more than 105 decibels?

A business owner is trying to decide whether to buy, rent, or lease office space and has constructed the following payoff table based on whether business is brisk or slow.

If the probability of brisk business is .40 and for slow business is .60, the expected value of perfect information is:

A group of friends are planning a recreational outing and have constructed the following payoff table to help them decide which activity to engage in. Assume that the payoffs represent their level of enjoyment for each activity under the various weather conditions.

Weather

Cold Warm Rainy

S1 S2 S3

Bike: A1 10 8 6

Hike: A2 14 15 2

Fish: A3 7 8 9

If the group chooses to minimize their maximum regret, what activity will they choose?

A business owner is trying to decide whether to buy, rent, or lease office space and has constructed the following payoff table based on whether business is brisk or slow.

The maximax strategy is:

A group of friends are planning a recreational outing and have constructed the following payoff table to help them decide which activity to engage in. Assume that the payoffs represent their level of enjoyment for each activity under the various weather conditions.

Weather

Cold Warm Rainy

S1 S2 S3

Bike: A1 10 8 6

Hike: A2 14 15 2

Fish: A3 7 8 9

What is the conservative decision for this situation?

A life insurance company wants to update its actuarial tables. Assume that the probability distribution of the lifetimes of the participants is approximately a normal distribution with a mean of 71 years and a standard deviation of 3.5 years. What proportion of the plan participants are expected to see their 75th birthday? *Note: Write your answers with two places after the decimal, rounding off as appropriate.*

A brand of television has a lifetime that is normally distributed with a mean of 7 years and a standard deviation of 2.5 years. What is the probability that a randomly chosen TV will last more than 8 years?*Note: Write your answers with two places after the decimal, rounding off as appropriate.*** **

A manager has developed a payoff table that indicates the profits associated with a set of alternatives under 2 possible states of nature.

Alt S1 S2

1 10 2

2 -2 8

3 8 5

What is the highest expected value? Assume that the probability of S2 is equal to 0.4.

The quality control manager for ENTA Inc. must decide whether to accept (a1), further analyze (a2) or reject (a3) a lot of incoming material. Assume the following payoff table is available. Historical data indicates that there is 30% chance that the lot is poor quality (s1), 50 % chance that the lot is fair quality (s2) and 20% chance that the lot is good quality (s3).

What is the numerical value of the minimax regret?

The quality control manager for ENTA Inc. must decide whether to accept (a1), further analyze (a2) or reject (a3) a lot of incoming material. Assume the following payoff table is available. Historical data indicates that there is 30% chance that the lot is poor quality (s1), 50 % chance that the lot is fair quality (s2) and 20% chance that the lot is good quality (s3).

What is the numerical value of the maximin?

A business owner is trying to decide whether to buy, rent, or lease office space and has constructed the following payoff table based on whether business is brisk or slow.

If the probability of brisk business is .40, what is the numerical maximum expected value?

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## A+ Tutorial for MAT540 - Quiz- WEEK 2

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### Question xx

xxxxxxxxxxxxxxx xxx percent xx all xxxxxxxxxxxx xxxx xxxxxx 1 xxxxxxxx xxxxxxxxx xx xxx xxxx if xxx data is xxxxxxxx distributed. � Answer | ||||

Selected Answer: False Correct xxxxxxx False |

### Question 2

xxxxxxxIf xxx xxxxxx xxx not mutually xxxxxxxxxx then P(A or B) = P(A) x xxxxxxx xxxxxx | ||||

Selected xxxxxxx xxxxxx Correct xxxxxxx xxxxxx |

### Question 3

xxxxxxxxxxxxxxxxxx xxxxx are used only to xxxxxxx conditional xxxxxxxxxxxxxx � xxxxxx | ||||

Selected Answer: xxxxxx Correct Answer: False |

### xxxxxxxx 4

xxxxxxxxxThe minimin xxxxxxxxx is optimistic. xxx Answer | ||||

xxxxxxx Answer: xxxxx |

### Question 5

xxxUsing the minimax xxxxxx criterion, xx first xxxxxxxxx x xxxxx xx regrets. xxxxxxxxxxxxx xxx each xxxxxxxx xxxxxxxxx xx xxxx xxxxxx xxx xxxxxx of nature xxx make a xxxx of xxx maximum regret xxxxxxxx xxx xxxx xxxxxxxxx We then xxxx xxx xxxxxxxx with the |

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