d. What is the probability that no more than 7 of the 15 students in your sample say that they have not received hurtful comments online in the past 30 days?

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This is my professor's solution to 33d and I just need an explanation for 33d.

Why didn't we find all values in the binomial probability table for Y less than or equal 7 and add them up like we did in 33c? Why did we find P(X>7)?

5.33 Cyberbullying. A survey of 4972 U.S. students aged 12 to 17 years reveals
that 25% have received mean or hurtful comments online in the past 30 days.¹⁹
You take a random sample of 15 undergraduates and ask them whether they
have received mean or hurtful comments online in the past 30 days. If the rate at
your university matches this 25% rate:
a. What is the distribution of the number of undergraduates who say that
they have received hurtful comments online in the past 30 days?
b. What is the distribution of the number of undergraduates who say that
they have not received hurtful comments online in the past 30 days?
c. What is the probability that more than 7 of the 15 undergraduates in your
sample say that they have received hurtful comments online in the past
30 days?
d. What is the probability that no more than 7 of the 15 students in your
sample say that they have not received hurtful comments online in the
past 30 days?
Transcribed Image Text:5.33 Cyberbullying. A survey of 4972 U.S. students aged 12 to 17 years reveals that 25% have received mean or hurtful comments online in the past 30 days.¹⁹ You take a random sample of 15 undergraduates and ask them whether they have received mean or hurtful comments online in the past 30 days. If the rate at your university matches this 25% rate: a. What is the distribution of the number of undergraduates who say that they have received hurtful comments online in the past 30 days? b. What is the distribution of the number of undergraduates who say that they have not received hurtful comments online in the past 30 days? c. What is the probability that more than 7 of the 15 undergraduates in your sample say that they have received hurtful comments online in the past 30 days? d. What is the probability that no more than 7 of the 15 students in your sample say that they have not received hurtful comments online in the past 30 days?
(5.33
p.320
ck: 15 (1) (4972) = 497.2 ⇒ binomial model is good,
a) X=# who have received mean comments, ~ (Bi(1525)
b) Y = # who haven't
~ Bi (15,75)
15) = ₂0393 +₁0131+.0034 +0007 +.0001 =
=60566
P(X>7) = P(8, 9, 10,
1
d) P(Y ≤ 7) = P(X) 17) =60566
Transcribed Image Text:(5.33 p.320 ck: 15 (1) (4972) = 497.2 ⇒ binomial model is good, a) X=# who have received mean comments, ~ (Bi(1525) b) Y = # who haven't ~ Bi (15,75) 15) = ₂0393 +₁0131+.0034 +0007 +.0001 = =60566 P(X>7) = P(8, 9, 10, 1 d) P(Y ≤ 7) = P(X) 17) =60566
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