Answer:
Step-by-step explanation:
1) As the sample size is 1,000 and there are 23 defectives in the output of the sample collected from Machine #1, the answer is 23/1000=0.023.
2) Estimate of the process proportion of defectives is the average of the proportion of defectives from all samples. In this case, it is : (23+15+29+13)/{4*(1000)}=80/4000=0.02.
3) Estimate of the Standard Deviation: Let us denote the mean (average) of the proportion of defectives by p. Then, the estimate for the standard deviation is : sqrt{p*(1 - p)/n}. Where n is the sample size. Putting p = 0.02, and n = 1000, we get: σ=0.0044.
4) The control Limits for this case, at Alpha risk of 0.05 (i.e. equivalent to 95% confidence interval), can be found out using the formulas given below:
Lower Control Limit : p - (1.96)*σ = 0.02 - (1.96)*0.0044=0.0113.
& Upper Control Limit: p + (1.96)*σ = 0.02 + (1.96)*0.0044 = 0.0287.
5) The proportion defective in each case is : Machine #1: 0.023; Machine #2: 0.015; Machine# 3: 0.029; Machine# 4: 0.013. For the Lower & Upper control limits of 0.014 & 0.026; It is easy to see that Machines #3 & #4 appear to be out of control.
When you write terms in denominator on numerator, sign of indices changes.
The amount paid to the man in the first year given the total he received in four years is $3,700.
<h3>Equation</h3>
- Amount paid in the first year = x
- Amount paid in the second year = (x + 500)
- Amount paid in the third year = x + 500 + 500
= (x + 1000)
- Amount paid in the fourth year = x + 500 + 500 + 500
= (x + 1500)
Total payment = first year + second year + third year + fourth year
x + (x + 500) + (x + 1000) + (x + 1500) = 17,800
x + x + 500 + x + 1000 + x + 1500 = 17800
4x + 3000 = 17,800
4x = 17,800 - 3000
4x = 14,800
x = 14,800/4
x = $3,700
Therefore, $3,700 was paid to the man in the first year.
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Answer:
K = 17
Based on the given conditions, formulate:
51 / 3 = k
Swap the sides : k = 51 / 3
Cross out the common factor: k = 17
