Consider the 63 automatic teller machine (ATM) transaction times given in Table

Question

Consider the 63 automatic teller machine (ATM) transaction times given in Table 3.4.

When we compute the sample mean and sample standard deviation for the transaction times, we find that x = 36.56 and s = 4.475. Compute each of the intervals [x ± s], [x ± 2s], and [x ± 3s]. Then count the number of transaction times that actually fall into each interval and find the percentage of transaction times that actually fall into each interval. (Round your answers to 3 decimal places. Omit the "%" sign in your response.)

ATM Transaction Times (in Seconds) for 63 Withdrawals Transaction Time 1 32 2 32 3 41 4 51 5 42 6 39 7 33 8 43 9 35 10 33 11 33 12 32 13 42 14 34 15 37 16 37 17 33 18 35 19 40 20 36 21 32 22 34 23 32 24 34 25 35 26 33 27 42 28 46 29 52 30 36 31 37 32 32 33 39 34 36 35 41 36 32 37 33 38 34 39 38 40 32 41 35 42 33 43 37 44 32 45 33 46 33 47 40 48 35 49 33 50 39 51 34 52 34 53 33 54 38 55 41 56 34 57 35 58 35 59 37 60 39 61 44 62 40 63 39

Explanation / Answer

Setting up the bounds,

x +/- s = 36.56 +/- 4.475 = (32.085, 41.035)

x +/- 2s = 36.56 +/- 2*4.475 = (27.61, 45.51)

x +/- 3s = 36.56 +/- 3*4.475 = (23.135, 49.985) [ANSWERS, INTERVALS]

Now, counting those who lie within the intervals, consider the table:

Interval Frequency (f) Relative Frequency (f/n)*100% (32.085, 41.035) 46 73.01587 (27.61, 45.51) 60 95.2381 (23.135, 49.985) 61 96.8254

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