Question

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How do people express laughter on Reddit? Researchers studied millions of posts on Reddit and isolated comments that used a
textual form of laughter such as "lol" or "haha" (emojis weren't included). Of the comments with a textual form of laughter,
55.8% used some form of "lol". Randomly select 300 comments on Reddit that use a textual form of laughter and let X = the
number of comments that use a variation of "lol."
(a) Show that the probability distribution of X is approximately normal.
and n(1-p)=
np=
The probability distribution of X is approximately normal because np and n(1-p) are both
(b) Calculate the mean of the appropriate normal distribution.
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Answer 1

The distribution of X is approximately normal because both np and n(1-p) are greater than 5. The mean of the distribution is 167.4 and the standard deviation is approximately 12.996.

Step-by-step explanation:

To justify that the probability distribution of X is approximately normal, we must check that both np and n(1-p) are greater than 5. Given that p = 0.558 (the probability of selecting a comment with 'lol'), for n = 300 comments:

• np = 300 * 0.558 = 167.4
• n(1-p) = 300 * (1 - 0.558) = 300 * 0.442 = 132.6

Since both np and n(1-p) are greater than 5, the distribution of X is approximately normal by the central limit theorem.

The mean (μ) of the normal distribution is equal to np:

Mean = np = 300 * 0.558 = 167.4

The standard deviation (σ) of the normal distribution is given by √(np(1-p)):

σ = √(300 * 0.558 * 0.442) = √(167.4 * 132.6) = approximately 12.996