# Mathematics

**Question 1**

1. A standard normal distribution has a mean of _____ and standard deviation of _____.

zero, zero | ||

zero, one | ||

one, one | ||

one, zero |

1 points

**Question 2**

1. The area under the normal curve between z = 0 and z = 1 is ________________ the area under the normal curve between z = 1 and z = 2.

Less than | ||

Greater than | ||

Equal to | ||

A, B, or C above dependent on the value of the mean | ||

A, B, or C above dependent on the value of the standard deviation |

1 points

**Question 3**

1. The MPG (Miles per Gallon) for a mid-size car is normally distributed with a mean of 32 and a standard deviation of .8. What is the probability that the MPG for a selected mid-size car would be: Less than 33.2?

43.32% | ||

6.68% | ||

93.32% | ||

86.64% | ||

13.36% |

1 points

**Question 4**

1. The fill weight of a certain brand of adult cereal is normally distributed with a mean of 910 grams and a standard deviation of 5 grams. If we select one box of cereal at random from this population, what is the probability that it will weigh less than 900 grams?

4772 | ||

.9772 | ||

.9544 | ||

.0228 | ||

.0456 |

1 points

**Question 5**

1. Which of the following statements is not a property of the normal probability distribution?

The normal distribution is symmetric. | ||

95.44% of all possible observed values of the random variable x are within plus or minus three standard deviations of the population mean. | ||

The mean, median, and mode are equal. | ||

The area under the normal curve to the right of the mean is equal to the area under the normal curve to the left of the mean. | ||

All of the above answers are properties of the normal distribution. |

1 points

**Question 6**

1. For a normal population with a mean of 10 and a variance 4, the *P*(*X* ≥ 10) is ___.

1.0 | ||

0.5 | ||

0.75 | ||

0.25 |

1 points

**Question 7**

1. The flying time of a drone airplane has a normal distribution with mean 4.76 hours and standard deviation of .04 hours. What is the probability that the drone will fly: Less than 4.66 hours?

-.0062 | ||

.5062 | ||

.0062 | ||

.9938 |

1 points

**Question 8**

1. What is the probability that a standard normal random variable will be between .3 and 3.2?

.6179 | ||

.3808 | ||

.6192 | ||

.9987 |

1 points

**Question 9**

1. An apple juice producer buys all his apples from a conglomerate of apple growers in one northwest state. The amount of juice squeezed from each of these apples is approximately normally distributed with a mean of 2.25 ounces and a standard deviation of 0.15 ounce. What is the probability that a randomly selected apple will contain between 2.00 and 3.00 ounces?

.0475 | ||

.4525 | ||

.9525 | ||

.9554 |

1 points

**Question 10**

1. The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.05 inches and a standard deviation of 0.2 inches. What is the probability that a sheet selected at random from the population is between 30.25 and 30.65 inches long?

.9987 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

.1574 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

.1587 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

.8413 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

Question 1
1. (Percentile) An apple juice producer buys all his apples from a conglomerate of apple growers in one northwest state. The amount of juice squeezed from each of these apples is approximately normally distributed with a mean of 2.25 ounces and a standard deviation of 0.15 ounce. 77% of the apples will contain at least how many ounces of juice?
1 points
1. (Percentile) An apple juice producer buys all his apples from a conglomerate of apple growers in one northwest state. The amount of juice squeezed from each of these apples is approximately normally distributed with a mean of 2.25 ounces and a standard deviation of 0.15 ounce. Between what two values (in ounces) symmetrically distributed around the population mean will 80% of the apples fall?
1 points
1. (Percentile) Find z when the area between 0 and z is .4750
1 points
1. (Percentile) Find z when the area to the right of z is .1314
1 points
1. (Percentile) Find z when the area to the left of z is .6700
1 points
1. (Percentile) Find z when the area between z and – z is .9030
1 points
1. (Percentile) The average time a subscriber spends reading the local newspaper is 49 minutes. Assume the standard deviation is 16 minutes and that the times are normally distributed. For the 10% who spend the most time reading the paper, how much time do they spend?
1 points |