In a high school with 5,000 students, the number of text messages sent by each student during a particular month was recorded. T
he 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?
Hi Question : <span>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?
4 x 51 ---------- 204
Answer : 204
I hope it helps and if it is correct please press brainlest ~Rie</span>
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.
