Question

10. Let *x* be the number of PC
computers are repaired at the Best Buy in Green Acres Mall on a
randomly selected day. This data is represented in the discrete
probably distribution table below

(x) |
1 |
2 |
3 |
4 |
5 |

P(x) |
0.16 |
0.22 |
? |
0.20 |
0.14 |

- Find the probability that 3 computers were repaired that day.
- Find the mean of this probability distribution
- Find the standard deviation of this probability distribution
- Find probability that at most 4 computers were repaired.

Answer #1

a)

Sum of probabilities equal to 1

P(X) = 1

0.16 + 0.22 + P(X = 3) + 0.20 + 0.14 = 1

0.72 + P (X = 3) = 1

**P (X = 3) = 0.28**

b)

Mean = x * P(X)

= 1 * 0.16 + 2 * 0.22 + 3 * 0.28 + 4 * 0.20 + 5 * 0.14

= **2.94**

c)

Standard deviation = Sqrt [ x^{2} *
P(X) - mean^{2} ]

= sqrt [ 1^{2} * 0.16 + 2^{2} * 0.22 +
3^{2} * 0.28 + 4^{2} * 0.20 + 5^{2} * 0.14
- 2.94^{2} ]

= **1.2714**

d)

P( X <= 4) = 1 - P(X = 5)

= 1 - 0.14

= **0.86**

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