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In: Statistics and Probability

Human Resource: It is believed that first-year salaries for newly fresh graduates follow a normal distribution...

Human Resource: It is believed that first-year salaries for newly fresh graduates follow a normal distribution with a standard deviation of RM2,500. A random sample of 29-B newly fresh graduates was chosen.

  1. Find the probability that the sample standard deviation is more than RM3,000.
  2. Find the probability that the sample standard deviation is less than RM1,500.

Solutions

Expert Solution

As the population is normal we use the chi-square distribution to find the required probabilities.

The chi-square variable is given as below

where n is the sample size, s is the sample standard deviation and is the population standard deviation. Hence we have the below

1. For the first case we have s=3000, n is 29 and is 2500. Hence we have the below

From chi-square distribution, the required probability for degrees of freedom of 28 is P(x >= 40.32) = 0.062

2. For the first case we have s=1500, n is 29 and is 2500. Hence we have the below

From chi-square distribution, the required probability for degrees of freedom of 28 P(x <= 10.08) is 0.00075

orchestra answered 1 year ago
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