Final answer:
In the scenario where x~N(5, 2.3), the mean μ is 5 and the standard deviation σ is √2.3. The curve's highest point is at x=5, the total area under the curve is 1, and calculations for specific probabilities or areas require a z-table or software.
Step-by-step explanation:
Suppose x~N(5, 2.3), where μ (mu) represents the mean of the normal distribution and σ (sigma) is the standard deviation. The variable μ would be 5, as it is the first number in the notation. The standard deviation, σ, would be the square root of the variance, so it is √2.3.
The highest point on the normal curve corresponds to the mean, so it would be directly above x=5. The total area under the curve of a normal distribution is always equal to 1, indicating a 100% probability that a value will fall somewhere under the curve.
To find the area to the left of 5.3, you would normally use a z-table or normal distribution calculator. However, since the value is very close to the mean, we can infer that the area would be slightly more than 0.5 (50%).
An x-value that is 1.5 standard deviations to the left of the mean can be calculated as x = μ - 1.5σ, which would be 5 - 1.5(√2.3). The computations involving the probability P(.v > 4) and P(4.7 < x < 6.01) require the use of a z-table or software to determine the areas under the normal curve representing these probabilities.