check the picture below.
so, y = -3 is simply a horizontal line, as you see there, and any perpendicular line to that will be a vertical one, whose slope is undefined.
we can check by simply picking two points off the red line hmmm say (-2,2) and (-2, -2)
Answer:
Since M1 has the higher probability of being in the desired range, we choose M1.
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Two machines M1, M2 are used to manufacture resistors with a design specification of 1000 ohm with 10% tolerance.
So we need the machines to be within 1000 - 0.1*1000 = 900 ohms and 1000 + 0.1*1000 = 1100 ohms.
For each machine, we need to find the probabilty of the machine being in this range. We choose the one with the higher probability.
M1:
Resistors of M1 are found to follow normal distribution with mean 1050 ohm and standard deviation of 100 ohm. This means that
The probability is the pvalue of Z when X = 1100 subtracted by the pvalue of Z when X = 900. So
X = 1100
has a pvalue of 0.6915.
X = 900
has a pvalue of 0.0668
0.6915 - 0.0668 = 0.6247.
M1 has a 62.47% probability of being in the desired range.
M2:
M2 are found to follow normal distribution with mean 1000 ohm and standard deviation of 120 ohm. This means that
X = 1100
has a pvalue of 0.7967.
X = 900
has a pvalue of 0.2033
0.7967 - 0.2033 = 0.5934
M2 has a 59.34% probability of being in the desired range.
Since M1 has the higher probability of being in the desired range, we choose M1.
Answer:
Point Estimate for different between population means = - 0.99
Step-by-step explanation:
We are given data of two samples and we have to find the best point estimate of the true difference between two population means. Remember that in absence of data about population the best estimator is the sample data. So, we will find the means of both sample data and find the difference of that means. This difference between the means of sample data will be the best point estimate for the true difference between the population means.
Formula to calculate the mean is:
Mean of Sample 1:
Mean of Sample 2:
Therefore the best point estimate for difference between two population means would be = Mean of Sample 1 - Mean of Sample 2
= 128.55 - 129.54
= - 0.99