A pair of dice is rolled 180 times. a) What is the probability that a total of 7 occurs at least 25 times?
b) What is the probability that a total of 7 occurs between 31 and 41 times inclusive?
b) What is the probability that a total of 7 occurs between 31 and 41 times inclusive?
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x is bin(180,1/6)
suitable for normal approximation to the binomial,
as n > 30 and both np & nq > 10
i'll solve part (a). you can solve part (b) similarly
a. µ = np = 180 *1/6
b. σ = sqrt(npq) = sqrt(180 *1/6 *5/6)
c. with continuity correction, at least 25 becomes at least 24.5
d. z = (24.5-µ)/σ
e. P(x ≥24.5) = P(z ≥ (24.5-µ)/σ) = .8643 <------
for (b), don't forget to compute for 30.5-41.5 with continuity correction
suitable for normal approximation to the binomial,
as n > 30 and both np & nq > 10
i'll solve part (a). you can solve part (b) similarly
a. µ = np = 180 *1/6
b. σ = sqrt(npq) = sqrt(180 *1/6 *5/6)
c. with continuity correction, at least 25 becomes at least 24.5
d. z = (24.5-µ)/σ
e. P(x ≥24.5) = P(z ≥ (24.5-µ)/σ) = .8643 <------
for (b), don't forget to compute for 30.5-41.5 with continuity correction
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7.9