Posted: September 17th, 2017

Paper Details

- The average number of annual trips per family to amusement parts in U.S is Poisson distributed, with mean of 0.7 trips per year. What is the probability of randomly selecting an American family and finding the following?
- The family did not make a trip to an amusement park last year.
- The family took exactly one trip to an amusement park last year.
- The family took two or more trips to an amusement park last year.
- The family took three or fewer trips to an amusement park last year.
- The family took exactly four trips to an amusement park last year.

- 20 wrist watches in a box of 100 are defective. If 10watches are selected at random, find the probability that (i) 10 aredefective (ii) 10 are good (iii) at least one watch is defective

(iv) at most 3 are defective. (v) exactly 3 are defective

(i) Find the area under the normal curve between z = 0 andz = 1.75

(ii) Find the area under the normal curve between z = -1.5 andz = 2.6

(iii) Find the area to the left side of z = 1.96

(iv) Find the area under the normal curve which lies to the rightof z = 2.70

(v) A normal distribution has mean = 50 and standard deviationis 8. Find the probability that x assumes a value between 34and 62

(vi)A normal distribution has mean = 20 and S.D = 10. Findarea between x =15 and x = 40

(vii) Given a normal curve with mean 30 and standard deviation Find the area under the curve between 26 and 40

- Calculate coefficient of correlation from the following data.

X | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 11 | 12 |

Y | 9 | 8 | 7 | 9 | 11 | 12 | 15 | 16 | 8 |

- According to the U. S Bureau of Labor statistics, the average weekly earnings of a production worker in 1997 were $ 424.20. Suppose a labor researcher wants to test to demine whether this figure is still accurate today. The researcher randomly selects 60 production workers from across the United States and obtains are preventative earnings statement for one week from each. The resulting sample average is $435.70. Assuming a population standard deviation of $ 33, and a 5% level of significance, determine whether the mean weekly earnings of a production worker have changed.

- The mean lifetime of 100 fluorescent light bulbs produced by a company is computed to be 1570 hours with a standard deviation of 120 hours. If m is the mean lifetime of all the bulbs

Produced by the company, test the hypothesis m=1600 hours against the alternative hypothesis m ¹ 1600 hours using a 5% level of significance.

7(a) On Saturdays, cars arrive at Sami Schmitt’s Scrub and Shine Car Wash at the rate of 6 cars per fifteen minute interval. The average interarrival time between cars is _____________.

- 2.167 minutes
- 10.000 minutes
- 0.167 minutes
- 2.500 minutes

(b) . On Saturdays, cars arrive at Sami Schmitt’s Scrub and Shine Car Wash at the rate of 6 cars per fifteen minute interval. The probability that at least 2 minutes will elapse between car arrivals is _____________.

- 0.0000
- 0.4493
- 0.1353
- 2.2255

( c ) On Saturdays, cars arrive at Sami Schmitt’s Scrub and Shine Car Wash at the rate of 6 cars per fifteen minute interval. The probability that at least 5 minutes will elapse between car arrivals is _____________.

- 0.0000
- 0.4493
- 0.1353
- 0.0067

(d) On Saturdays, cars arrive at Sami Schmitt’s Scrub and Shine Car Wash at the rate of 6 cars per fifteen minute interval. The probability that less than 10 minutes will elapse between car arrivals is _____________.

- 0.8465
- 0.9817
- 0.0183
- 0.1535

8 ( a) If *x* is uniformly distributed over the interval 8 to 12, inclusively (8 *x* 12), then the P(9 *x* 11) is __________________.

- 0.250
- 0.500
- 0.333
- 1.000

(b ) If *x* is uniformly distributed over the interval 8 to 12, inclusively (8 *x* 12), then the P(10.0 *x* 11.5) is __________________.

- 0.250
- 0.333
- 0.375
- 0.000

( c ) If *x* is uniformly distributed over the interval 8 to 12, inclusively (8 *x* 12), then the P(13 *x* 15) is __________________.

- 0.250
- 0.500
- 0.375
- 0.000

( d ) If *x* is uniformly distributed over the interval 8 to 12, inclusively (8 *x* 12), then P(*x*< 7) is __________________.

- 0.500
- 0.000
- 0.375
- 0.250

( e ) If *x* is uniformly distributed over the interval 8 to 12, inclusively (8 *x* 12), then P(*x* 11) is __________________.

- 0.750
- 0.000
- 0.333
- 0.500

( f ) If *x* is uniformly distributed over the interval 8 to 12, inclusively (8 *x* 12), then P(*x* 10) is __________________.

- 0.750
- 0.000
- 0.333
- 0.500

(9) Using exponential smoothing (i) with *a* = 0.20 (ii) with *a* = 0.80

July | 12 |

Aug | 5 |

Sept | 7 |

Oct | 11 |

Compute

- the forecast value for August
- the forecast value for September
- the forecast value for October
- the forecast value for November
- Mean Absolute Deviation (MAD)
- Mean Square Error (MSE)
- Mean Percentage Error (MPE)
- Mean Absolute Percentage Error (MAPE)
- Mean Error (ME)

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