Which equation has a constant of proportionality equal to 5? A. y = 5x

B. y = 10/5x

C. y = 5/25x

D. y = 1/2x

A

Step-by-step explanation:

The standard equation of proportion is

y = kx ← k is the constant of proportionality

A

y = 5x is in this form with k = 5

B

y = x = 2x with k = 2 ≠ 5

C

y = x = x with k = ≠ 5

D

y = x with k = ≠ 5

(a)

The standard deviation is  

(b)

Here sample size is large and np and n(1-p) are both greater than 30. So we can use a normal approximation of binomial distribution. z-score for Y = 234.5 (using continuity correction) is  

So the approximate probability that at least 235 people in the sample will still be in the Rewards Program after the first four weeks is  

Step-by-step explanation:  

Let X is a random variable that shows the number of people who would drop out of the Rewards Program within four weeks. Here X has binomial distribution with parameters n = 300 and p = 0.18.

(a)  

The mean number of people who would drop out of the Rewards Program within four weeks in a sample of this size is  

The standard deviation is  

(b)  

Let Y is a random variable that shows the number of people in the sample who will still be in the Rewards Program after the first four weeks. Here Y has a binomial distribution with parameters n= 300 and p=0.82. So mean of Y is  

Here sample size is large and np and n(1-p) are both greater than 30. So we can use a normal approximation of binomial distribution. z-score for Y = 234.5 (using continuity correction) is

So the approximate probability that at least 235 people in the sample will still be in the Rewards Program after the first four weeks is