Assignment 3

Assignment 3 Question10of12 @ To determine the distribution of the height of female grade 6 students in a developing country, a researcher collected height data (in inches) from one grade 6 class and reported them as follows: 55 55 62 59 54 55 54 51 52 51 62 58 58 62 51 70 58 63 62 53 65 66 59 50 51 Calculate the mean, median and mode. M ean = 57.44 @ Round to 2 decimal places Solution The correct answer is 57.44. T Meanz% 55+ 55+ 62+ 59 + 54 + 55 + 54 + 51 + 52 + 51 + 62 + 58 + 58 + 62 + 51 + 70 N 25 1,436 25 = 57.44 Median = 58| @

The correct answer is 58. Sort the values: 50,51,51,51,51,52, 53, 54, 54, 55, 55, 55, 58, 58, 58, 59, 59, 62, 62, 62, 62, 63, 65, 66, 70 We find the middle most element. Since there are 25 elements, then ? = 12.5 ~ 13. Therefore, the median is the 13th value which is 58. X X Mode : | 51*/ & * Solution The correct answers are 51,62. Question20f12 @ The frequency table shows the number of items returned daily for a refund at a convenience store over the last 28 days of operation: Number of items frequency Returned f x) o v s wN o o h = © Determine the mean, median, and mode.

2841 1 s Location of median: L,, = The median is halfway between terms 14 and 15 in the array. From the Cumulative Freqency column, Term 14: 4 Term 15: 5 Therefore, the median is 4.5. Mode: 2| @ Question30f12 ® What percent of data would you expect to find a. above the 90" percentile? - Solution The correct answer is 10%. b. below the 23" percentile? Solution The correct answer is 23%.

c. between the 45™ and 82" percentiles? % © Solution The correct answer is 37%. Question4of12 @ The following data consists of birth weights (pounds) of a sample of newborn babies at a local hospital: 75 86 72 89 80 82 69 92 96 79 74 Calculate the following: a. Range Range = 27| @ b. Variance Round to 2 decimal places Solution The correct answer is 0.75. c. Standard Deviation Round to 2 decimal places

Question6of12 @ Given Samples A and B below, Sample A: 4.7 4.3 37 23 21 4.7 4.9 4.1 Sample B: 4.5 2.0 4.1 3.6 2.4 3.6 2.8 3.7 a. Calculate the mean and standard deviation for each sample. sampleA: 5 = 379 @ss = 103 @ sampleB: i3 = 3%| @33 = ox| @ Sample A: 34.1 X = & =— =379 n Sa? - (21)2 & = n n—1 2 137.77 — (341) - 9 N 9-1 =1.0711 33 3.5

Sample B: 30.2 == ="" 33 n 9 2 . (X % A & = n—1 2 106.52— (302) B 9 B 9-1 = 0.6478 s = /0.6478 = 0.80 Question7o0f12 ©® The recommended minimum credit card payment for a sample of 100 credit card holders is summarized below: Minimum Payment ($) | Frequency 15 to under 30 35 | 30 to under 45 31 B 45 to under 60 17 60 to under 75 5 75 to under 90 12 a. Estimate the mean minimum payment. Mean: Round to 2 decimal places.

d. Describe the shape of the distribution in terms of symmetry/skewness. Skewness: | Positively Skewed v] @ Solution The correct answer is the first option, Positively Skewed. The mean is 41.7 and the median is 37.5, then mean > median. Therefore, the distribution is positively skewed. Question 8 of 12 Asearch on Best Barryo Mobile's website for "smartwatch" produced ninety-two results, 40 of which are actual smartwatches. Their prices are summarized in the frequency table below: Price ($) Number of Watches 50 to under 100 4 100 to under 150 4 150 to under 200 200 to under 250 250 to under 300 12 300 to under 350 a. Calculate an approximate value for the sample variance.

The correct answer is 5,883.01. Price ($) i (Midpoint) f | fx fr2 50 to under 100 75 4 | 300 | 22,500 100 to under 150 125 4 | 500 | 62500 150 to under 200 175 9 | 1575 | 275625 200 to under 250 225 6 | 1350 | 303,750 250 to under 300 275 | 12 | 3300 | 907,500 300 to under 350 325 | 5 | 1625 | 528125 Total - 40 | 8650 | 2,100,000 a2 - (X f=)? st = n n—1 2 2,100,000 — (380" B 401 — 5,883.01 b. Calculate an approximate value for the sample standard deviation. Round to two decimal places if necessary Solution The correct answer is 76.70.

Question100f12 ® Outgoing calls at a call centre are completed in 130 seconds on average with a standard deviation of 8 seconds. Suppose call completion times are approximately normal. The shortest 2.5% of the completed calls will last less than how many seconds? seconds © Solution The correct answer is 114 seconds. Question 11 of 12 The hourly pay of a sample of city bus drivers has a mean of $42.50 and a standard deviation of $2.75. If the distribution of the data is unknown, determine what percent of the drivers make between $28.75 and $56.25? e Solution The correct answer is 96%.

Question 12 of 12 Incoming calls to the main line at a call centre are transferred within an average of 45 seconds with a standard deviation of 4 seconds. Find an interval (in seconds) centered around the mean, during which at least 36% of the calls are transferred. Solution (Dseconds The correct answer is 40 seconds — 50 seconds . The shape of the distribution is unknown. A 1 proportion =1 — k_z 1 036=1— 2 1 036 =1— 2 1 —0.64 = _fi k? = 1.5625 k=125 z1=p —ko z1 =45 —1.25(4) x1 = 40 o= p +ko x9 =45+ 1.25 (4) xs =50