Compare what you get for P(> b)
2-score:
Z = \frac{72 - 69}{3} = 1
5
From the standard normal table, P(Z < 1) lapprox 0.8413
6
So, P(X > 72) = 1 - 0.8413 = 0.1587                                                                                                        Draw the normal distributions (using the same scale on the x-axis (so the distributions should be getting narrower) and shade in the area corresponding to P(> b)

Here is the plot of two normal distributions:

1. **Blue curve**: Represents the normal distribution with \( \mu = 69 \) and \( \sigma = 3 \), which is the distribution relevant to your problem.
2. **Green curve**: Represents the standard normal distribution with \( \mu = 0 \) and \( \sigma = 1 \), shown for comparison.

The shaded blue area corresponds to \( P(X > 72) \), which equals \( 0.1587 \), and it is the area under the curve to the right of \( X = 72 \) (indicated by the red dashed line).

Would you like further clarification or additional details?

Here are five related questions for further exploration:
1. How does changing the mean affect the shape and position of the normal distribution curve?
2. What happens to the probability \( P(X > 72) \) if the standard deviation increases?
3. Can you calculate the probability \( P(X < 66) \) for the same distribution?
4. How would you calculate the probability for a range, such as \( P(67 < X < 72) \)?
5. What is the relationship between the Z-score and the probability for normal distributions?

**Tip**: In normal distributions, about 68% of values fall within one standard deviation of the mean.

Compare what you get for P(> b)
2-score:
Z = \frac{72 - 69}{3} = 1
From the standard normal table, P(Z < 1) ≈ 0.8413
So, P(X > 72) = 1 - 0.8413 = 0.1587
Draw the normal distributions (using the same scale on the x-axis and shade in the area corresponding to P(> b))

Learn how to calculate the probability P(X > 72) using normal distribution and Z-scores. This problem includes the Z-score formula, standard normal table lookup, and drawing normal distributions with shaded regions. Suitable for students in Grades 10-12.

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