(a) The daily sales of a product in different shops follow a normal distribution. The targeted mean of the daily sales o
Posted: Wed Apr 27, 2022 1:28 pm
(a) The daily sales of a product in different shops follow a
normal distribution. The targeted mean of the daily sales of the
product and their variance in the population are K10,000 and K2,500
respectively. The sales manager of the company which produces the
product feels that the sales of the product has improved in the
recent past. A random sample of 49 shops is taken from the normal
population for which the mean daily sales is found to be
K9,600.Check whether the sales of the product in different shops
has really improved at a significance level of 0.05.
(b) The weight of cement bags produced in a cement company
follow normal distribution whose population is infinite. The
expected mean of weight of the cement bags for sales of this
population is 45KG and its variance is unknown. The sales manager
of the firm claims that the mean weight of the cement bags is
significantly more than the expected mean weight of the population.
So, he has selected a random sample of 36 bags and its mean and
variance are found to be 44KG and 1.25KG, respectively. Verify the
intuition of the sales manager at a significance level of 0.05.
(c) The quality manager of a washing machine company feels that
the mean time between failures of the motors received is at most 90
days. The quality manager wants to test his intuition. Hence, he
has taken a sample of 25 motors whose mean time between failure and
its variance are found to be 93 days and 16 days, respectively.
Verify the intuition of the quality manager at a significance level
of 0.05.
normal distribution. The targeted mean of the daily sales of the
product and their variance in the population are K10,000 and K2,500
respectively. The sales manager of the company which produces the
product feels that the sales of the product has improved in the
recent past. A random sample of 49 shops is taken from the normal
population for which the mean daily sales is found to be
K9,600.Check whether the sales of the product in different shops
has really improved at a significance level of 0.05.
(b) The weight of cement bags produced in a cement company
follow normal distribution whose population is infinite. The
expected mean of weight of the cement bags for sales of this
population is 45KG and its variance is unknown. The sales manager
of the firm claims that the mean weight of the cement bags is
significantly more than the expected mean weight of the population.
So, he has selected a random sample of 36 bags and its mean and
variance are found to be 44KG and 1.25KG, respectively. Verify the
intuition of the sales manager at a significance level of 0.05.
(c) The quality manager of a washing machine company feels that
the mean time between failures of the motors received is at most 90
days. The quality manager wants to test his intuition. Hence, he
has taken a sample of 25 motors whose mean time between failure and
its variance are found to be 93 days and 16 days, respectively.
Verify the intuition of the quality manager at a significance level
of 0.05.