Calculate using Standard Normal Table: P(22 <= X <= 25) = .4332

It explains how to use the formula for a normal distribution and how to find the probability using the table. In summary, the conversation provides step-by-step instructions for using the standard normal table to calculate to four decimal places.
  • #1
Uniman
11
0
Using the standard normal table in your lecture notes, calculate to four decimal places

Table

file:///Users/manukumarindia/Desktop/Screen%20Shot%202012-10-29%20at%2011.12.15%20AM.png

Work done so far.

If X ~ N(22,4), z = (x - 22)/sqrt(4) ~ N(0,1) Thus, P(22 <= X <= 25) = P((22-22)/2 <= z <= (25-22)/2) = P(0 <= z <= 1.5) = P(z <= 1.5) - P(Z <= 0) Now, we use the table above. P(z <= 1.5) - P(Z <= 0) = .9332 - .5 = .4332​
 
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  • #2
Uniman said:
Using the standard normal table in your lecture notes, calculate to four decimal places

Table

file:///Users/manukumarindia/Desktop/Screen%20Shot%202012-10-29%20at%2011.12.15%20AM.png

Work done so far.

If X ~ N(22,4), z = (x - 22)/sqrt(4) ~ N(0,1) Thus, P(22 <= X <= 25) = P((22-22)/2 <= z <= (25-22)/2) = P(0 <= z <= 1.5) = P(z <= 1.5) - P(Z <= 0) Now, we use the table above. P(z <= 1.5) - P(Z <= 0) = .9332 - .5 = .4332​

That seems OK.

CB
 

FAQ: Calculate using Standard Normal Table: P(22 <= X <= 25) = .4332

What does the equation P(22 <= X <= 25) = .4332 represent?

The equation represents the probability of a value falling between 22 and 25 in a normal distribution, with a mean of 0 and a standard deviation of 1. The value of .4332 is the area under the curve between 22 and 25.

How do you use the Standard Normal Table to calculate this probability?

The Standard Normal Table is a table of values that corresponds to the area under the curve of a standard normal distribution. To calculate the probability, you need to find the z-scores for 22 and 25, which represent the number of standard deviations away from the mean. Then, find the corresponding values in the table and subtract the smaller value from the larger value to get the probability.

Why is it important to use a Standard Normal Table for calculations?

The Standard Normal Table allows us to easily calculate probabilities for a normal distribution without having to use complex equations. It is a useful tool for scientists and statisticians to analyze and interpret data.

What is the significance of the value .4332 in this equation?

The value .4332 represents the area under the curve between 22 and 25 in a standard normal distribution. This can be interpreted as the probability of a random variable falling between those two values. In other words, there is a 43.32% chance of a value falling between 22 and 25 in a normal distribution with a mean of 0 and a standard deviation of 1.

Can the Standard Normal Table be used for any normal distribution?

No, the Standard Normal Table can only be used for a normal distribution with a mean of 0 and a standard deviation of 1. For other normal distributions, we would need to use a different table or statistical software to calculate probabilities.

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