The length of time needed to complete a certain test is normally distributed with mean 92 minutes and standard deviation 8 minutes. Find the probability that it will take less than 80 minutes to complete the test.

The probability that it will take less than 80 minutes

  P(X≤80) = 0.0768        

Step-by-step explanation:

Step(i):-

Given mean of the Population = 92 minutes

Given standard deviation of the Population = 8 minutes

Let 'X' be the random variable in normal distribution

Let 'X' = 80 minutes

Step(ii):-

The probability that it will take less than 80 minutes

P(X≤80) = P(Z≤-1.5)

            =  0.5 - A(1.5)

            = 0.5 - 0.4232

           =0.0768

Final -

The probability that it will take less than 80 minutes

  P(X≤80) = 0.0768        

total amount of money that he should pay if he has not used his duty free exemption is $98

step-by-step explanation:

given a united states citizen returning to the states declares the following items at the customs office: 3 shirts at $8.50 each 2 dresses at $27.50 each 1 pair of gold cuff links at $17.50 per pair. we have to find how much he pay

cost of 3 shirts if one cost at $8.50 is

cost of 2 dresses if one cost at $27.50 is  

cost of 1 pair of gold cuff at $17.50

so, total amount of money that he should pay if he has not used his duty free exemption is   $25.5+$55+$17.50=$98

step-by-step explanation:

to find if any function is an inverse of the other, put the first equation in as x in the next one. then simplify and solve. if at the end you get the statement y = x, then it is an inverse. if you get anything else, it is not.