QUANTITATIVE ANALYSIS

Quantitative Analysis



Quantitative Analysis

Answer No.1

Answer No.1a

The above graph is obtained from MS. Excel for checking the Normality in the data. The shape of the graph represents the Normal distribution, so we can say that data is Normal.

Answer No 1b

We have first used the formula that is. We have used this formula for answering this question as

The proportion of the population that falls into the “gifted” category is 0.021.

Answer No.1c

We have again first used the formula that is. We have used this formula for answering this question as

So, the proportion of the population that falls into the “genius” category is 0.0016.

Answer No. 1d

The minimum score above the 99.9th percentile is 145.947. This is obtained by applying the formula in Excel “=PERCENTILE(F5:F6058,0.999)”

Answer No. 1e

We will first use the formula of Normal distribution that is ) so

Then we have seen its value by Normsdist command on Excel by the formula =Normsdist(-0.4082). The result obtained is 0.00002. The probability that the average IQ of the sample is below 95 is 0.00002.

Answer No. 1f

For this as part as well we have first used the formula so,

Then we have again seen its value by Normsdist command on Excel by the formula =Normsdist(35.925). The result obtained is 1. The probability that the average IQ of the sample is above 144 is 1-1=0.

Answer No. 1g

The difference between the value obtain in part c differs from the probability value in part f is because of the fact that the sample size that we have selected is quite small than the population data that we have and as we know that as sample size increases the accuracy of the answer also increases.

Answer No. 2

Answer No. 2a.i

The confidence interval of the true mean is calculated by the formula

So,

The confidence interval for the sample size 30 is

The claim that manufacturer had made is that the mean life time of the screens is 56,475 hours.

Answer No. 2b.i

As, this time is lying between the confidence interval that we have obtained, so we can challenge the manufacturer claim in a way that although the mean time obtained is lower than the 58000 hours but still the time they have obtained is lying between the confidence interval limit. Indeed the mean time manufacturer have calculated is on the basis of the sample of 30 screens.

Answer No. 2c.i

The probability of screen failed after 52500 hours is 0.1356.

Answer No. 2a.ii

No, the population ...