The number X of days in the summer months that a construction crew cannot work because of the weather has the probability distribution x 6 7 8 9 10 P (x) 0.03 0.08 0.15 0.20 0.19 x 11 12 13 14 P (x) 0.16 0.10 0.07 0.02 a. Find the probability that no more than ten days will be lost next summer. b. Find the probability that from 8 to 12 days will be lost next summer. c. Find the probability that no days at all will be lost next summer.

a.) The probability of losing no more than ten days next summer is

0.65

b.) The probability that 8 - 12 days will be lost next summer is 0.8

c.) The probability there will be no days lost next summer is 0.

Step-by-step explanation:

The probability distribution for the number X of days in the summer that a construction crew cannot work because of the weather is given below:

x P (x)

6 0.03

7 0.08

8 0.15

9 0.2

10 0.19

11 0.16

12 0.1

13 0.07

14 0.02

a.) To find the probability that no more than 10 days will lost next summer can be found by adding the values of probability of the days lost which are 10 days or less, that is to say we can write

p (x ≤ 10) = p (x=6) + p (x = 7) + p (x=8) + p (x=9) + p (x=10)

= 0.03 + 0.08 + 0.15 + 0.2 + 0.19

= 0.65

b.) To find the probability that 8 to 12 days will be lost next summer will be given by taking into account and adding the probabilities starting form the probability when 8 days are lost to the probability when 12 days are lost

p (8 ≤ x ≤ 12) = p (x=8) + p (x=9) + p (x=10) + p (x=11) + p (x=12)

= 0.15 + 0.2 + 0.19 + 0.16 + 0.1

= 0.8

c.) The probability that no days will be lost next summer will be given by

= 1 - (p (x=6) + p (x=7) + p (x=8) + p (x=9) + p (10) + p (11) + p (12))

= 1 - 1

= 0

The probability that will be no days lost next summer is zero. We can conclude that there will be some days lost next summer.