There are 46 students in an elementary statistics class. On the basis of years of experience, the instructor knows that the time needed to grade a randomly chosen first examination paper is a random variable with an expected value of 5 min and a standard deviation of 4 min. (Round your answers to four decimal places.)(a) If grading times are independent and the instructor begins grading at 6:50 P. M. and grades continuously, what is the (approximate) probability that he is through grading before the 11:00 P. M. TV news begins?(b) If the sports report begins at 11:10, what is the probability that he misses part of the report if he waits until grading is done before turning on the TV?

a) P ( T < 250 mins ) = 0.7695

b) P ( T > 260 mins ) = 0.1344

Step-by-step explanation:

- The RV from a sample has the following parameters that are mean = 5 mins, and standard deviation s = 4 mins.

- The entire population has n = 46 students.

- We will first compute the population mean u and population standard deviation σ as follows:

                            u = n*mean

                            u = 46*5 = 230 mins

                            σ = sqt ( n ) * s

                            σ = sqt ( 46 ) * 4

                            σ = 27.129 mins

- Approximating that the time taken T to grade the population of entire class follows a normal distribution with parameters u and σ as follows:

                            T~ N ( 230 , 27.129 )

Find:

- If grading times are independent and the instructor begins grading at 6:50 P.M. and grades continuously, what is the (approximate) probability that he is through grading before the 11:00 P.M. TV news begins?

- The total time till 6:50 PM to 11:00 PM is ( 4 hr and 10 mins ) = 250 mins.

- We will compute the Z-value as follows:

                        Z = ( 250 - 230 ) / 27.129

                        Z = 0.7372

- Then use the Z-Tables and determine the probability:

                        P ( T < 250 mins ) = P ( Z < 0.7372 )

                        P ( T < 250 mins ) = 0.7695

Find:

-  If the sports report begins at 11:10, what is the probability that he misses part of the report if he waits until grading is done before turning on the TV?

- For the teacher to miss the sports report he must take more time than 6:50 PM to 11:10 P.M.

- The total time till 6:50 PM to 11:10 PM is ( 4 hr and 20 mins ) = 260 mins.

- We will compute the Z-value as follows:

                        Z = ( 260 - 230 ) / 27.129

                        Z = 1.10582

- Then use the Z-Tables and determine the probability:

                        P ( T > 260 mins ) = P ( Z > 1.10582 )

                        P ( T > 260 mins ) = 0.1344

answer

explanation

the area of a circle is calculated using the formula

or

we can use any of the above formulae to calculate the required. preferably, let us use the latter since the diameter is

we substitute the diameter into the formula to get:

this is the exact value for the area of the circle.

the correct answer is a

where is the figure