An investment of 11,000 is made into an account that earns 4.25% annual compound interest for 30 months. Assuming no other deposits or withdrawal are made, what is the total value of the account after 30 months? A: $12,206.27

B: $13,412.54

C: 11,000

D: 1,206.27

It should be $12168.75

Step-by-step explanation:

First, converting R percent to r a decimal

r = R/100 = 4.25%/100 = 0.0425 per year,

then, solving our equation

I = 11000 × 0.0425 × 2.5 = 1168.75

I = $ 1,168.75

The simple interest accumulated

on a principal of $ 11,000.00

at a rate of 4.25% per year

for 2.5 years is $ 1,168.75.

1,168.75 + 11000 = 12168.75

a) P(x=108)=0.0020

b) P(x≥108)=0.9980

c) P(x<124)=0.7794

d) P(124≤x≤128)=0.1925

Step-by-step explanation:

We know the population proportion, that is p=0.84.

We take a sample of size n=143.

We will use the normal approximation to the binomial distribution to model this problem.

The mean and standard deviation of the normal approximation to the binomial distribution will be:

a) We have to calculate the probability that exactly 108 flights are on time.

As the normal distribution considers the random variable to be continous, we have to apply the continuity correction factor.

In this case, the probability of 108 flights on time can be calculated as P(107.5<x<108.5):

b) Now we have to calculate that at least 108 flights are on time.

As the probability includes 108, the continuity factor will indicates that we calculate P(x>107.5). The z-value for x=107.5 has been already calculated in point a:

c) We have to calculate the probability that fewer than 124 flights are on time. According to the continuity factor, we have to calculate the probability P(x<123.5), as the flight number 124 is not included in the interval.

d) We have to calculate the probability that between 124 and 128 flights, inclusive, are on time.

This interval corresponds to the probability P(123.5<x<128.5)