In a high school with 5,000 students, the number of text messages sent by each student during a particular month was recorded. the mean number of text messages sent during the month was 55 per student. if the data was normally distributed, and if the standard deviation of the data was 4 text messages, which of these is the best estimate for the number of students who sent fewer than 51 text messages during the month?

The answer is 800

Step-by-step explanation:

Since the data is normally distributed, 68% of the data is within 1 standard deviation of the mean. This means that 68% of the students sent between 55 – 4, or 51, and 55 + 4, or 59 text messages during the month. For this reason, 32% of the students did not send between 51 and 59 text messages during the month. Half of the 32% sent fewer than 51 text messages, and the other half of the 32% sent more than 59 text messages. Therefore, since 16% of the 5,000 students sent fewer than 51 text messages, a valid expectation for the number of students who sent fewer than 51 text messages during the month is 800.

f(x) has value 150 at x= 0

and 0 at x= 3

so d(f(x))/dt = slope = -150/3 = -50