# 4. The level of support for corporate sustainability (measured on a quantitative scale ranging from0 to 160 points) was obtained for each of 992 senior managers at CPA firms. The mean of thelevel of support was 67.755 with a standard deviation of 26.871. It can be shown that level ofsupport is approximately normally distributeda) Find the probability that the level of support for corporate sustainability of a randomly selectedsenior manager is less than 40 points.b) Find the probability that the level of support for corporate sustainability of a randomly selectedsenior manager is between 40 and 120 points.c) Find the probability that the level of support for corporate sustainability of a randomly selectedsenior manager is greater than 120 pointsd) One-fourth of the 992 senior managers indicated a level of support for corporate sustainabilitybelow what value?

Question

a,b,c

Step 1

Standard normal distribution:

The standard normal distribution is a special case of normal distribution. The standard normal distribution will have mean 0 and standard deviation 1. If a random variable y follows normal distribution with mean (m) and standard deviation (s), then the standard normal variable z will be as given below:

Step 2

a.

Find the probability that the level of support for corporate sustainability of a randomly selected senior manager is less than 40 points:

Denote the random variable x as level of support for corporate sustainability.

Given that the variable x follows normal distribution with mean 67.755 and standard deviation 26.871.

That is, E(x) = 67.755 and S.D(x) = 26.871.

Here, the requirement is that the level of support for corporate sustainability of a randomly selected senior manager should be less than 40 points.

That is, x < 40.

The probability that the level of support for corporate sustainability of a randomly selected senior manager is less than 40 points is obtained as 0.15151 from the calculation given below:

Step 3

b.

Find the probability that the level of support for corporate sustainability of a randomly selected senior manager lies between 40 and 120 points:

Here, the requirement is that the level of support for corporate sustainability of a randomly selected senior manager should lie between 40 and 120 points....

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