1.Find P(Z<-1.97 or Z>2.5),P(-2.08<Z<2.08) and P(0<Z<1.73)
2.The masses of packages from a particular machine are normally distributed with mean 200g and standard deviation 2g. Find the probability that a randomly selected package from the production line of the machine weighs i.less than 197g.
This webpage is a must if you are studying this topic and your up-to-date textbook
no longer has normal distribution tables in the back
http://davidmlane.com/normal.html
for the first one, find P(z < -1.97) and P(z > 2.5), then add them up
for the 2nd and 3rd, use the "between" button
Can you explain the second one?
The web site shows you how to use the area to the right of a point. Now do to the left of a point.
To answer these questions, we need to use the standard normal distribution table or a statistical software to find the probabilities associated with the standard normal distribution. The standard normal distribution has a mean of 0 and a standard deviation of 1.
1. P(Z < -1.97 or Z > 2.5):
To find this probability, we need to find the area under the standard normal distribution curve outside the range of -1.97 to 2.5. We can break it down into two parts: P(Z < -1.97) and P(Z > 2.5).
Using the standard normal distribution table or a statistical software, we can find the values for P(Z < -1.97) and P(Z > 2.5). We can then sum these two probabilities to get the total probability.
2. P(-2.08 < Z < 2.08):
To find this probability, we need to find the area under the standard normal distribution curve between -2.08 and 2.08. We can calculate this by subtracting P(Z < -2.08) from P(Z < 2.08).
Using the standard normal distribution table or a statistical software, we can find the values for P(Z < -2.08) and P(Z < 2.08). We can then subtract the smaller probability from the larger one to get the desired probability.
3. P(0 < Z < 1.73):
To find this probability, we need to find the area under the standard normal distribution curve between 0 and 1.73. We can calculate this by subtracting P(Z < 0) from P(Z < 1.73).
Using the standard normal distribution table or a statistical software, we can find the values for P(Z < 0) and P(Z < 1.73). We can then subtract the smaller probability from the larger one to get the desired probability.
For the second part of your question:
The masses of packages from a particular machine are normally distributed with a mean of 200g and a standard deviation of 2g.
To find the probability that a randomly selected package from the production line weighs less than 197g, we need to standardize the value and then find the corresponding probability using the standard normal distribution table or a statistical software.
Let X be the weight of a randomly selected package. We can standardize X using the formula:
Z = (X - μ) / σ,
where Z is the standardized value, μ is the mean, and σ is the standard deviation.
In this case, we have X = 197g, μ = 200g, and σ = 2g. Plugging these values into the formula, we get:
Z = (197 - 200) / 2 = -1.5.
Now we can use the standard normal distribution table or a statistical software to find the probability P(Z < -1.5), which represents the probability that a randomly selected package weighs less than 197g.