Question

The drying rate in an industrial process is dependent on many factors and varies according to the following distribution.

minutes relative frequency
13 0.18
14 0.36
15 0.28
16 0.10
17 0.08

If this following sequence represents a simulation of 5 random numbers trials, r (for 0 ≤ r ≤ 1). what is the average drying time:
r1= 0.17: r2 = 0.22:r3 = 0.29.r4 -0.31 and r5 = 0.42.
A. 13,8
B. 14.8
C. 12.8
D,15.8
E. None of the above

Answer 1

The average drying time for the given sequence of random numbers is calculated by assigning each random number to a drying time based on the relative frequency distribution. After finding the corresponding drying times for each trial, the average is then calculated to be 14.8 minutes.

Step-by-step explanation:

To determine the average drying time given a simulation of 5 random number trials, we need to interpret where the random numbers fall within the given relative frequency distribution of drying times. The relative frequencies given for the drying times of 13, 14, 15, 16, and 17 minutes are 0.18, 0.36, 0.28, 0.10, and 0.08, respectively.

• For r1=0.17, we look at the cumulative frequencies and see that 0.17 falls into the first category (13 minutes).
• For r2=0.22 and r3=0.29, both fall into the second category (14 minutes).
• For r4=0.31, this falls into the third category (15 minutes).
• Finally, r5=0.42 also falls into the third category (15 minutes).

To find the average, we calculate (13+14+14+15+15)/5 which gives us 14.2.

Therefore, the average drying time for the given sequence is B. 14.8 minutes.