Using the standard normal table in your lecture notes, calculate to four decimal places
Uniman said:
Table
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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
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.
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.
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.
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.
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.