Answer:
a. 0.8366
b. No
Step-by-step explanation:
We will use the central limit theorem which can be applied to a random sample from any distribution as long as the mean and the variance are both finite and the sample size is large (the sample size n should be greater than 30). Here we have that the tip percentage at the restaurant has a mean value of 18% and a standard deviation of 6%, then because of the central limit theorem, we know that the sample mean tip percentage is approximately normally distributed with mean 18% and standard deviation
.
a. The z-score related to 16% is given by (16-18)/0.9487 = -2.1081 and the z-score related to 19% is given by (19-18)/0.9487 = 1.0541. We are looking for
b. If the sample size had been 15 rather than 40, then, the probability requested in part (a) could not be calculated from the given information, this because the central limit theorem only applies when the sample size is large, for example n > 30.
Answer:
35 students in the class.
Step-by-step explanation:
If there are 5 students in the class, then 2 of them would wear glasses and 3 of them wouldn't. (Equation 1)
Now, there are 14 students how are wearing glasses.
We just times the whole Equation 1 by 7.
If there are 5 x 7 = 35 students in the class, then 2 x 7 = 14 of them would wear glasses and 3 x 7 = 21 of them wouldn't.
So, there are 35 students.
Answer:
![\sqrt[n]{x^a}=x^{a/n}](https://tex.z-dn.net/?f=%5Csqrt%5Bn%5D%7Bx%5Ea%7D%3Dx%5E%7Ba%2Fn%7D)
Step-by-step explanation:
While the "law"
![\sqrt[n]{x^n}=x](https://tex.z-dn.net/?f=%5Csqrt%5Bn%5D%7Bx%5En%7D%3Dx)
may seem more applicable, and may seem to be a special case of the law shown in the answer above, it is not true in general. For example, ...

Using the z-table, the probability that a student taking this test will finish in 100 minutes or less is 0.0824 or 8.24%.
For a normally distributed set of data, given the mean and standard deviation, the probability can be determined by solving the z-score and using the z-table.
First, solve for the z-score using the formula below.
z-score = (x – μ) / σ
where x = individual data value = 100
μ = mean = 125
σ = standard deviation = 18
z-score = (100 – 125) / 18
z-score = (-25) / 18
z-score = -1.39
Find the probability that corresponds to the z-score in the z-table. (see attached images)
-1.39 - (-1.3) : -1.4 - (-1.3) = x - 0.0968 : 0.0808 - 0.0968
-0.09 : -0.1 = x - 0.0968 : -0.016
x - 0.0968 = -0.09(-0.016)/-0.1
x = -0.0144 + 0.0968
x = 0.0824
x = 0.0824
Hence, the probability that a student taking this test will finish in 100 minutes or less is 0.0824 or 8.24%.
Learn more about probability here: brainly.com/question/26822684
#SPJ4