Question

Suppose that the probability that it rains on Friday is 80% and the probability that it rains on Saturday is 70%, and the event that it rains on Friday is independent of the event that it rains on Saturday. Find the probability that it DOES NOT RAIN on Friday and it DOES NOT RAIN on Saturday.

A sample of five scores was taken. They were 82, 73, 61, 97, and 83. Find the SAMPLE standard deviation of the scores. (Round to 2 decimal places).
The scores on a nationwide are normally distributed with a mean of 120 and a standard deviation of 20. Find the probability that a randomly selected test-taker scored less than 105. (Round to 4 decimal places)

Answer 1

0.06 (6%)

13.31

0.2266

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