2. based on data from ac nielsen, among households in the united states, the mean number of tv sets is 2.24, with a standard deviation of 1.38. a random sample of 40 households is selected. a. describe the sampling distribution of the sample mean number of tv sets in a sample of 40 households. state the shape of the distribution and check any necessary conditions for that. state the mean and compute the standard deviation (round to 4 decimal places). (6 pts.) b. in a random sample of 40 households, what is the probability that the sample mean is 2.55 or higher? include a sketch. show all work. (8 pts.)

Therefore the mean number of sample of 40 households results in 102 television sets is 2.55 & the probability of that the sample mean is 2.55 or higher is 0.412

What is probability?

The likelihood of an event happening is determined by probability. We may need to forecast an event's result in a variety of real-world circumstances. The outcomes of an event may be certain or uncertain to us. In these situations, we state that there is a likelihood that the event will occur or not.

Here,

Given:

mean number of tv sets (n)= 2.24

standard deviation ([tex]{S_d} }[/tex]) = 1.38

sample of 40 households results in 102 television sets so ,

mean number (n') = 102/40 =2.55

its mean number =2.55

the probability that the sample mean is 2.55 or higher

=> Z = [tex]\frac{n^{'}-n }{S_d} }[/tex]

=> Z =(2.55-2.24)/1.38

=>Z = 0.2246

the normal distribution of probability =

P=[tex]\frac{1 *e^{\frac{-1}{2}Z^{2} } }{\alpha \sqrt{2\pi } }[/tex]

P=0.588

therefore P(x<2.55)=0.588

=>P(2.55< x)= 1-0.588=0.412

Therefore the probability of that the sample mean is 2.55 or higher is 0.412

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