Question

5. The number of daily texts sent by Marymount students are normally distributed with a mean of 80 texts and a standard deviation of 50 texts.

(a) Find the probability that a randomly selected Marymount student sends more than 100 texts each day.

(b) Find the probability that 25 randomly selected Marymount students will have a mean number of daily texts sent that is greater than 50 texts.

(c) Suppose a parent wants their child in the bottom 25% of texters. Find the cut-off value for the number of texts below which 25% of MCU students lie.

if possible include graph

Answer 1

Q.5) Given that, mean (μ) = 80 texts and

standard deviation = 50 texts

a) We want to find, P(X > 100)

Therefore, required probability is 0.3446

b) sample size (n) = 25

We want to find,

Therefore, required probability is 0.9987

c) We want to find, the value of x such that, P(X < x) = 0.25

Therefore, the cut-off value for the number of texts below which 25% of MCU students lie is 46.5