THE DISTRIBUTION OF THE NUMBER OF VIEWERS FOR THE AMERICAN IDOL TELEVISION SHOW FOLLOWS A NORMAL DISTRIBUTION WITH A MEAN OF 29 MILLION AND A STANDARD DEVIATION OF 5 MILLION. WHAT IS YHE PROBABILITY NEXT WEEKS SHOW WILL: HAVE AT LEAST 23 MILLION

Please do not use all caps. Not only is it harder to read, but it is like SHOUTING online. Thank you.

Z = (score-mean)/SD

Calculate without the six zeros to indicate millions to make it easier.

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability related to the Z score.

To find the probability that next week's show will have at least 23 million viewers, we need to standardize the value and use the standard normal distribution.

Here's how you can calculate it step by step:

Step 1: Standardize the value using the formula:
Standardized value (Z) = (X - mean) / standard deviation
In this case, X = 23 million, mean = 29 million, and standard deviation = 5 million.
So, Z = (23 - 29) / 5 = -1.2

Step 2: Look up the standardized value in the standard normal distribution table (also known as the Z-table) to find the corresponding probability.
The Z-table provides the area under the curve up to a given standardized value.

Looking up -1.2 in the Z-table, we find that the area to the left of -1.2 is approximately 0.1151.

Step 3: Calculate the probability of having at least 23 million viewers.
Since we want at least 23 million viewers, we need to find the area to the right of -1.2 in the standard normal distribution.
We can do this by subtracting the area to the left of -1.2 from 1.
Probability = 1 - 0.1151 = 0.8849

Therefore, the probability that next week's show will have at least 23 million viewers is approximately 0.8849 or 88.49%.