(a)
The shape of the Normal distribution is symmetrical bell shape with 99.7% of the data falls within 3 standard deviations from the mean. This means, a value less than 3 standard deviations from the mean is possible with a non-zero probability.
= 2.14 - 3 * 1.38 = -2
So, number of television is -2 has a non-zero probability, which is not possible as the number of televisions in a household cannot be a negative number.
This, the shape of the distribution of televisions in a household does not follow normal distribution.
(b)
Mean number of televisions = 102 / 40 = 2.55
(c)
By Central limit theorem, the sample mean will follow normal distribution with mean = 2.24 and = 0.218
Probability of obtaining the sample mean of 2.55 = P( = 2.55)
= P(Z = (2.55 - 2.24) / 0.218)
= P(Z = 1.42)
= 0.1456
Since the obtained probability is not low (not below 0.05), the statistic in part (b) is possible if the population mean is 2.24 and thus the statistic does not contradict the results reported by AC Nielsen.
7. Number of Televisions Based on data obtained from AC Nielsen, the mean number of televisions in a household in...
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