12. A drawer contains 2 red socks, 6 white socks,
1 answer:
Answer:
Probability that first sock is blue is 0.33 and Probability that second sock is red is 0.16
Step-by-step explanation:
Number of red socks = 2
Number of white socks = 6
Number of blue socks = 4
Total socks in drawer = 2+6+4 = 12
The formula used to calculate probability is:
We are given you draw out a sock, return it, and draw out a second sock.
We need to find the probability that the first sock is blue and the second sock is red?
Using formula:
Probability that first sock is blue = 4/12 = 1/3 = 0.33
Probability that second sock is red = 2/12 = 1/6 = 0.16
So, Probability that first sock is blue is 0.33 and Probability that second sock is red is 0.16
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The solution to the system of equations is (8, -4)
<h3>How to solve the system?</h3>The system of equations is given as;
y = -1/4x - 2
y = 3/8x - 7
See attachment for the graph of the equations
From the attached graph, we have the point of intersection to be
(x, y) = (8, -4)
Hence, the solution to the system of equations is (8, -4)
Read more about system of equations at:
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Complete question is;
A shareholders’ group, in lodging a protest, claimed that the mean tenure for a chief executive office (CEO) was at least seven years. A survey of companies reported in The Wall Street Journal found a sample mean tenure of x¯ = 7.27 years for CEOs with a standard deviation of s = 6.38 years (The Wall Street Journal, January 2, 2007).
a. Formulate hypotheses that can be used to challenge the validity of the claim made by
the shareholders’ group.
b. Assume 85 companies were included in the sample. What is the p-value for your hypothesis
test?
Answer:
A) Null hypothesis: H0: μ ≥ 7
Alternative hypothesis: μ < 7
B) p-value = 0.3488
Step-by-step explanation:
A) We are told that the shareholders group claimed that the mean tenure for a chief executive office (CEO) was at least seven years.
Thus, defining the hypothesis, we have;
Null hypothesis: H0: μ ≥ 7
Alternative hypothesis: μ < 7
B) Sample mean: x¯ = 7.27 years standard deviation: s = 6.38 years
Sample size = 85
Formula for the test static is;
t = (x¯ - μ)/(s/√n)
t = (7.27 - 7)/(6.38/√85)
t = 0.39
From online p-value from t score calculator attached using: t = 0.39, DF= 85 - 1 = 84, significance value = 0.05, one tail, we have;
p-value = 0.3488
