Question

The “Eyland Krew”; Lola(No Waay!), Dai Lejai(Ghet Da Stat Out!), Mayra(Oh Shift!)and Leslie(Smak Dat Stat), wanted to find the number of tune-ups per month necessary for the new TSEGAsports car. They sent their top executive RandDominic(of “RejectTim,he’s Shady!”) and they came up with the following results:

Tune-ups: 0 1 2 3 4 5 6

Probability: .05 .10 .30 .16 .23 .12 .04

Find:

a.(2pts.)The probability that theTSEGAsports car needed no less than 3tune-ups in a month.

b.(6pts.)Find the variance and the standard deviation for the number of tune-ups in a month.

c.(3pts.)What was the average number of tune-ups per month?

Answer 1

Given data:

Tune-ups:	0	1	2	3	4	5	6
Probability:	0.05	0.1	0.3	0.16	0.23	0.12	0.04

a)

probability for the TSEGAsports car neededno less than 3 tuneups in a month

means : its required atmost 3

P(tuneups >= 3) = P(3)+P(4)+P(5)+P(6)

= 0.16+ 0.23+0.12+0.04

= 0.55

The probability that theTSEGAsports car needed no less than 3tune-ups in a month is 0.55

b)

Variance ,

is the mean (Average)of the tunes per month

								Total
Tune-ups:	0	1	2	3	4	5	6
Probability:	0.05	0.1	0.3	0.16	0.23	0.12	0.04	1
X*p	0	0.1	0.6	0.48	0.92	0.6	0.24	2.94
X^2 * p	0	0.1	1.2	1.44	3.68	3	1.44	10.86

the variance = 2.2164

the standard deviation = 1.4888

c)

average number of tune-ups per month is 2.94