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)

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

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.

answer is 144

step-by-step explanation: