Hi,
l'm stuck on these problems..need help.
1) Suppose yu have conversations with yo friend on 100 diff topics. On any given topic there's a 0.02 prob that yu agree. If yu did agree on a topic yu wld consider it a coincidence.
a)Find the probability that yu and yo friend never agree on any two topics on these 100 topics, given that whether yu agree on any 2 different topics are independent events.
b) Find the prob thAay yu have a coincidence on at least one topic.
2) Arestaurant charges $8,95 per customer. Their expense per customer has a distribution that is skewed to the right with a mean of 8.20 and s=3
a) If 100 cust on a particualr day have characteristics of a random sample, find the mean and standard error of the sampling distribution of their sample mean expense per cust.
b) Find the prob that restaurant makes a profit that day, with the sample mean expense being less than 8,95. ( Hint:Apply the central limit theorem to the sampling distribution in (a).
(a) It's a Binomial distribution problem. You don't agree with prob 1-0.02=0.98 so the prob that you don't agree on any topic is 0.98^100.
(b) This is the same as the prob that you don't disagree on every topic, i.e. 1-P(agree on no topic/disagree on every topic).
2.
a) From the central limit theorem:
M = 8.3
Standard Error = variance / (sqrt n)
= 3 / sqrt (100)
= .30
b)
z = X - u / Std Error
= 8.95 - 8.20 / .30
= 2.5
find the area P ( z < +2.5) in your normal table, multiply it by 100, thats your percent.
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