Answer:
0.06 (6%)
13.31
0.2266
Step-by-step explanation:
1)
Given that :
Probability that it rains on Friday ; P(FR) = 0.8
Probability that it rains on Saturday ; P(SR) = 0.7
P(FR) and P(SR) are independent events
Probability that it does not rain on Friday ; P(FR)' = 1 - P(FR) = 1 - 0.8 = 0.2
Probability that it does not rain on Saturday ; P(SR)' = 1 - P(SR) = 1 - 0.7 = 0.3
Hence, probability that it does not rain on Friday and on Saturday ;
P(FR)' * P(SR)' = 0.2 * 0.3 = 0.06 = 0.06 * 100% = 6%
2)
Given the scores :
82, 73, 61, 97, 83 ;
The sample standard deviation :
Sqrt(Σ(X - m)^2 ÷ n - 1)
n = sample size = 5
m = mean = ΣX / n
m = (82 + 73 + 61 + 97 + 83) / 5 = 79.2
Sqrt((82 - 79.2)^2 + (73 - 79.2)^2 + (61 - 79.2)^2 + (97 - 79.2)^2 + (83 - 79.2)^2) / (5 - 1)
Sqrt(177.2) = 13.311649
Hence, standard deviation = 13.31
3.)
Given that :
Mean(m) = 120
Standard deviation (s) = 20
Probability that randomly taken test taker scores less than 105
P(x < 105)
Obtain the standardized score :
Z = (x - m) / s
Z = (105 - 120) / 20
Z = - 15 / 20
Z = - 0.75
P(Z < - 0.75) = 0.22663 (Z probability calculator)
= 0.2266
