How many real solutions does the following equation have?
1 answer:
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Answer:
Step-by-step explanation:
Given that:
population mean = 10
standard deviation = 0.1
sample mean = 9.8 < x > 10.2
The z score can be computed as:
if x > 10.2
z = 2
If x < 9.8
z = -2
The p-value = P (z ≤ 2) + P (z ≥ 2)
The p-value = P (z ≤ 2) + ( 1 - P (z ≥ 2)
p-value = 0.022750 +(1 - 0.97725)
p-value = 0.022750 + 0.022750
p-value = 0.0455
Therefore; the probability of defectives = 4.55%
the probability of acceptable = 1 - the probability of defectives
the probability of acceptable = 1 - 0.0455
the probability of acceptable = 0.9545
the probability of acceptable = 95.45%
4.55% are defective or 95.45% is acceptable.
sampling distribution of proportions:
sample size n=1000
p = 0.0455
The z - score for this distribution at most 5% of the items is;
z = 0.6828
The p-value = P(z ≤ 0.6828)
From the z tables
p-value = 0.7526
Thus, the probability that at most 5% of the items in a given batch will be defective = 0.7526
The z - score for this distribution for at least 85% of the items is;
z = −15.86
p-value = P(z ≥ -15.86)
p-value = 1 - P(z < -15.86)
p-value = 1 - 0
p-value = 1
Thus, the probability that at least 85% of these items in a given batch will be acceptable = 1
Correct Answer:
C option: 6 feet
Solution:
Since <span>Yolanda wants to keep the pool in proportion to the model, the ratio of diameter to depth of model and the pool will be same.
Let the depth of pool is x feet. So we can write:
Ratio of Diameter to Depth of Model = Ratio of Diameter to Depth of pool
</span>
<span>
This means the depth of pool should be 6 feet if </span><span>Yolanda wants to keep the pool in proportion to the model.</span>
C option: 6 feet
Solution:
Since <span>Yolanda wants to keep the pool in proportion to the model, the ratio of diameter to depth of model and the pool will be same.
Let the depth of pool is x feet. So we can write:
Ratio of Diameter to Depth of Model = Ratio of Diameter to Depth of pool
</span>
<span>
This means the depth of pool should be 6 feet if </span><span>Yolanda wants to keep the pool in proportion to the model.</span>