Please help me ASAP a newspaper publishes the following headline: if the weather is sunny this weekend then the kite festival wi
ll take place.
When the weekend arrives, the kite festival is taking place, so you conclude that the weather must be sunny. However, it is raining. What is the error in logic?
When the weekend arrives, the kite festival is taking place, so you conclude that the weather must be sunny. However, it is raining. What is the error in logic?
1 answer:
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Answer:
(a) The distribution of is a Binomial distribution.
(b) The sampling distribution of the sample mean will be approximately normal.
(c) The value of is 0.50.
Step-by-step explanation:
It is provided that random variables are independent and identically distributed Bernoulli random variables with <em>p</em> = 0.50.
The random sample selected is of size, <em>n</em> = 100.
(a)
Theorem:
Let be independent Bernoulli random variables, each with parameter <em>p</em>, then the sum of of thee random variables,
is a Binomial random variable with parameter <em>n</em> and <em>p</em>.
Thus, the distribution of is a Binomial distribution.
(b)
According to the Central Limit Theorem if we have an unknown population with mean <em>μ</em> and standard deviation <em>σ</em> and appropriately huge random samples (<em>n</em> > 30) are selected from the population with replacement, then the distribution of the sample mean will be approximately normally distributed.
The sample size is large, i.e. <em>n</em> = 100 > 30.
So, the sampling distribution of the sample mean will be approximately normal.
The mean of the distribution of sample mean is given by,
And the standard deviation of the distribution of sample mean is given by,
(c)
Compute the value of as follows:
*Use a <em>z</em>-table.
Thus, the value of is 0.50.