Answer:
The chance of completing the entire package installation in under 12 minutes is 0.1271.
Step-by-step explanation:
We define X as a normal distribution representing the time taken in seconds to install the software. According to the Central Limit Theorem, X is approximately normal, where the mean is 15 and variance is 15, giving a standard deviation of √15 = 3.873.
To find the probability of the total installation lasting less than 12 minutes, which equals 720 seconds, each installation should average under 720/68 = 10.5882 seconds. Thus, we seek the probability that X is less than 10.5882. To do this, we will apply W, the standard deviation value of X, calculated via the formula provided.
Utilizing 
, we reference the cumulative distribution function of the standard normal variable W, with values found in the attached file.
Given the symmetry of the standard normal distribution density function, we ascertain 
.
Consequently, the probability that the installation process for the entire package is completed within 12 minutes is 0.1271.
Answer: refer to the image
Step-by-step explanation:
Response:
$144,843.5
Detailed explanation:
In this scenario, we will utilize the compound interest formula
A= P(1+r)^t
A = final amount
P = initial principal
r = interest rate
t = number of periods
Given parameters
P= $27,000
R= 7.25%= 7.25/100= 0.0725
T= 24
A=27000(1+0.0725)^24
A= 27000(1.0725)^24
A= 27000*5.364
A= $144,843.5
By the end of 24 years, her account balance will reach $144,843.5
In 1980, if there were N individuals aged 100 or older, then by 2010, the number grew to N*1.66 for those 100 and above. A straightforward conditional expression can be framed as: If P, then Q, where P represents the hypothesis and Q is the conclusion. We understand that "The count of individuals aged 100 years or older increased by about 66% from 1980 to 2010," meaning that if we had N individuals aged 100 or older in 1980, we will have N*(166%/100%) = N*1.66 in 2010, allowing us to write a conditional statement: If there were N individuals aged 100 years old in 1980, then by 2010, we had N*1.66 individuals who were at least 100 years old.
