Answer: a) α = 0.7927, b) at u=14.8, β = 0.99767, at u = 14.9, β= 0.2073
Step-by-step explanation: a) from the question, u= population mean = 15 and x= sample mean = 14.9
σ = population standard deviation = 0.5, n = sample size = 50.
We get the probability of committing a type 1 error by using the z score.
Z = x - u/(σ/√n)
Z = 14.9 - 15/(0.5/√50)
Z = - 0.1/0.0707
Z = - 1.41.
By checking the the probabilistic value attached to this z score using a standard normal distribution table whose area is to the left of the distribution, we have that
P(z=-1.41) = 0.7927.
Hence the probability of committing a type 1 error is 0.7927
b)
at x = 14.8 ( I let ua=x=14.8)
Z = x - u/(σ/√n)
Z = 14.8 - 15/(0.5/√50)
Z = - 0.2/ 0.0707
Z = - 2.83
Using the standard normal distribution table, we have that
P(z=-2.38) = 0.00233.
But α + β = 1
Where α= probability of committing a type 1 error
β = probability of committing a type 2 error.
β = 1 - α
β = 1 - 0.00233
β = 0.99767
At x = 14.9
Z = x - u/(σ/√n)
Z = 14.9 - 15/(0.5/√50)
Z = - 0.1/0.0707
Z = - 1.41.
P(z=-1.41) = 0.7927.
α = 0.7927.
But α + β = 1
β = 1 - 0.7927
β = 0.2073
The answer is nearly 124 cm square
7/10 is 17th term of sequence a₁₆ = 1/5, d= 1/2.
Given the 16th term and the common difference, we add the common difference from the 16th term to determine the 17th term:
a₁₇ = a₁₆ + d
= 1/5 + 1/2
= 7/10
<h3>How to solve an equation?</h3>
To solve linear equations, utilize the steps that are provided below.
- Remove parentheses from each side of the equation and combine similar terms to make it simpler.
- To separate the variable term on one side of the equation, use addition or subtraction.
- To find the variable, use division or multiplication.
- The common denominator can be multiplied by each side of the equation to eliminate fractions.
Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
Learn more about linear equations
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Colby and Cheryl work in different local supermarkets. Colby regu-
larly earns $8.90 per hour, and he is paid time-and-a-half for each
hour of overtime he works. Cheryl regularly earns $7.10 per hour,
and she is paid double time for an hour of overtime. Who earns
more for one hour of overtime? How much more?
