Answer:
Our answer is 0.8172
Step-by-step explanation:
P(doubles on a single roll of pair of dice) =(6/36) =1/6
therefore P(in 3 rolls of pair of dice at least one doubles)=1-P(none of roll shows a double)
=1-(1-1/6)3 =91/216
for 12 players this follows binomial distribution with parameter n=12 and p=91/216
probability that at least 4 of the players will get “doubles” at least once =P(X>=4)
=1-(P(X<=3)
=1-((₁₂ C0)×(91/216)⁰(125/216)¹²+(₁₂ C1)×(91/216)¹(125/216)¹¹+(₁₂ C2)×(91/216)²(125/216)¹⁰+(₁₂ C3)×(91/216)³(125/216)⁹)
=1-0.1828
=0.8172
Complete question is;
A researcher wished to compare the average amount of time spent in extracurricular activities by high school students in a suburban school district with that in a school district of a large city. The researcher obtained a simple random sample of 60 high school students in a large suburban school district and found the mean time spent in extracurricular activities per week to be six hours with a standard deviation of three hours. The researcher also obtained an independent simple random sample of 40 high school students in a large city school district and found the mean time spent in extracurricular activities per week to be four hours with a standard deviation of two hours. Let x¯1 and x¯2 represent the mean amount of time spent in extracurricular activities per week by the populations of all high school students in the suburban and city school districts, respectively. Assume two-sample t procedures are safe to use?
what is the 95% confidence interval a researcher wishes to compare the average amount of time spent in extracurricular?
Answer:
CI = (0.755, 3.245)
Step-by-step explanation:
For SRS of 60;
Mean: x1¯ = 6
Standard deviation: s1 = 3
For SRS of 40;
Mean: x2¯ = 4
Standard deviation; s2 = 2
Critical value for the confidence interval of 95% is: t = 1.96
Formula for the CI is;
CI = (x¯1 - x¯2) ± t√[(s1²/n1) + ((s2)²/n1)]
Plugging in the relevant values, we have:
CI = (6 - 4) ± 1.96√[(3²/60) + ((4)²/40)]
CI = 2 ± 1.96√[(3²/60) + ((4)²/40)]
CI = 2 ± 1.96√0.55
CI = 2 ± 1.245
CI = [(2 - 1.245), (2 + 1.245)]
CI = (0.755, 3.245)
Answer:
1/9 9:1 9 to 1
1/4 1:4 1 to 4
Step-by-step explanation:
