Joshua currently earns $5000 a year from his lawn care business. He has two plans to increase his revenue. Plan 1 would increase
1 answer:
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Answer:
Colour | Probability
YELLOW | 0.20
WHITE | 0.18
GREEN | 0.12
RED | 0.18
BLUE | 0.32
Step-by-step explanation:
The complete question is presented on the attached image to this solution.
From the image of the spinner and the given probabilities, the combination of YELLOW, WHITE and GREEN make up exactly half of the total space on the spinner.
0.2 + 0.18 + 0.12 = 0.50
Then, BLUE and RED make up the other half of the spinner.
Probability of landing on either BLUE or RED = 1 - 0.50 = 0.50
Let P(BLUE) = x and P(RED) = y
x + y = 0.50
Two of the lines shown on the diagram are diameters of the circle.
The first line that is a diameter splits the circle into two parts; (WHITE, YELLOW, GREEN) and (RED, BLUE).
From here, we have established that x + y = 0.50
The other line that is a diameter splits The circle into two part; (WHITE, BLUE) and (YELLOW, GREEN, RED)
From this other information,
P(WHITE) + P(BLUE) = 0.50
0.18 + x = 0.50
x = 0.50 - 0.18 = 0.32
P(YELLOW) + P(GREEN) + P(RED) = 0.50
0.20 + 0.12 + y = 0.50
y = 0.50 - 0.32 = 0.18
To check, x + y = 0.32 + 0.18 = 0.50 (Correct!!)
Hope this Helps!!!
Answer:
99% confidence interval for the given specimen is [3.4125 , 3.4155].
Step-by-step explanation:
We are given that a laboratory scale is known to have a standard deviation (sigma) or 0.001 g in repeated weighing. Scale readings in repeated weighing are Normally distributed with mean equal to the true weight of the specimen.
Three weighing of a specimen on this scale give 3.412, 3.416, and 3.414 g.
Firstly, the pivotal quantity for 99% confidence interval for the true mean specimen is given by;
P.Q. = ~ N(0,1)
where, = sample mean weighing of specimen =
= 3.414 g
= population standard deviation = 0.001 g
n = sample of specimen = 3
= population mean
<em>Here for constructing 99% confidence interval we have used z statistics because we know about population standard deviation (sigma).</em>
So, 99% confidence interval for the population mean, is ;
P(-2.5758 < N(0,1) < 2.5758) = 0.99 {As the critical value of z at 0.5% level
of significance are -2.5758 & 2.5758}
P(-2.5758 < < 2.5758) = 0.99
P( <
<
) = 0.99
P( <
<
) = 0.99
<u>99% confidence interval for</u> = [
,
]
= [ ,
]
= [3.4125 , 3.4155]
Therefore, 99% confidence interval for this specimen is [3.4125 , 3.4155].