Normal Distribution Argumentative: Challenge and Solution Essay Example
The objective is to determine the likelihood of selecting a measurement between 19 and 31 from a normally distributed population with an average of 25 and a variance of 9. In order to accomplish this, we must convert the values 19 and 31 into their respective z values using the transformation formula for X to z (where µ = 25 and ?^2 = 9). The calculations demonstrate that z19 = (19 - 25) / v9 = -2 and z31 = (31 - 25) / v9 = +2. By determining the area between z = ±2, we can establish the desired probability.
4772) = 0.9554. Therefore, the chance of a randomly chosen measurement falling between 19 and 31 is approximately 0.95. This probability applies to both the X values and the z values. The area between 19 and 31, as well as the area between -2 and +2
..., is represented by a standard normal curve. Admission into a specific university relies on a nationwide exam with scores that follow a normal distribution having a mean of 500 and a standard deviation of 100. Tom's goal is to get accepted into this university, and he understands that he needs to outperform at least 70% of the test-takers.
Tom received a score of 585 on the test, and the question is whether this score meets the university's admission criteria. To evaluate this, we can utilize the random variable x to represent scores. The distribution of x follows a normal distribution with an average of 500 and a standard deviation of 100. The area beneath the normal curve corresponds to the number of students who took the test.
By multiplying the areas
under the curve by 100, we can express them as percentages. For instance, if x equals 585, we can convert it to z with the formula z = (x - 500) / 100. This conversion results in z = 0.85. The proportion P of students who scored below 585 can be determined by calculating the area to the left of z = 0.85. This calculation yields P = 0.8023 or equivalently, P = 80%.
23% of the students who took the test will be admitted to this University, and Tom scored better than 80.
