Answer :
Approximately 0.13% of the values lie above 38 in this normal distribution.
To find the percentage of values that lie above 38 in a normal distribution with a mean of 23 and a standard deviation of 5, we can use the 68-95-99.7 rule.
Step 1: Calculate the z-score.
The z-score represents the number of standard deviations away from the mean a particular value is. We can calculate the z-score using the formula:
z = (x - μ) / σ
where x is the value (in this case, 38), μ is the mean (23), and σ is the standard deviation (5). Plugging in the values:
z = (38 - 23) / 5 = 3
Step 2: Determine the percentage using the z-score.
The z-score tells us the percentage of values below a given value in a standard normal distribution. However, since we want the percentage above 38, we need to subtract the percentage below 38 from 100%.
From the standard normal distribution table, we find that the percentage below a z-score of 3 is approximately 0.9987. Therefore, the percentage above 38 is:
100% - 0.9987% ≈ 0.13%
Therefore, approximately 0.13% of the values lie above 38 in this normal distribution.
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The percentage of values that lie above 38 in this normal distribution is approximately 0.15%.
To solve this problem
We need to assume a normal distribution.
Approximately 68% of the values in a normal distribution, according to the rule, are within one standard deviation of the mean.
Two standard deviations from the mean are occupied by about 95% of the data.
Three standard deviations from the mean are where 99.7% of the data fall.
In this instance, the standard deviation is 5, and the mean is 23. We're looking for the proportion of numbers that are higher than 38.
Step 1: Calculate the z-score for the value 38.
z = (x - mean) / standard deviation
z = (38 - 23) / 5
z = 3
Step 2: Determine the percentage of values above 38.
The z-score of 3 indicates that there are three standard deviations above the mean. Only 0.15% of the values (0.15% + 0.15% + 0.15% = 0.45%) deviate more than three standard deviations from the mean, according to the 68-95-99.7 criterion.
So, the percentage of values that lie above 38 in this normal distribution is approximately 0.15%.
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