Suppose that the weights of vans delivering goods to inner city shops are normally Distributed.If 70% of the vans weigh more than 1200 kg, and 80% weigh more than 1000 kg, What are the mean and standard deviation for the weights of vans serving the inner city
(round to tens)?
A) $\mu = 1510 \mathrm {~kg} ; \sigma = 620 \mathrm {~kg}$
B) $\mu = 1530 \mathrm {~kg} ; \sigma = 630 \mathrm {~kg}$..
C) $\mu = 1550 \mathrm {~kg} ; \sigma = 640 \mathrm {~kg}$
D) $\mu = 1530 \mathrm {~kg} ; \sigma = 630 \mathrm {~kg}$.
E) There is not enough information given to determine the mean and standard deviation.

Question

Suppose that the weights of vans delivering goods to inner city shops are normally Distributed.If 70% of the vans weigh more than 1200 kg, and 80% weigh more than 1000 kg, What are the mean and standard deviation for the weights of vans serving the inner city
(round to tens)? 
A) $\mu = 1510 \mathrm {~kg} ; \sigma = 620 \mathrm {~kg}$
B) $\mu = 1530 \mathrm {~kg} ; \sigma = 630 \mathrm {~kg}$..
C) $\mu = 1550 \mathrm {~kg} ; \sigma = 640 \mathrm {~kg}$
D) $\mu = 1530 \mathrm {~kg} ; \sigma = 630 \mathrm {~kg}$.
E) There is not enough information given to determine the mean and standard deviation.

Quizplus · Accepted Answer

The z-scores corresponding to 70% and 80% can be used to set up equations to solve for the mean and standard deviation. Solving these equations gives the mean and standard deviation as approximately 1530 kg and 630 kg, respectively.

Suppose That the Weights of Vans Delivering Goods to Inner μ=1510 kg;σ=620 kg\mu = 1510 \mathrm {~kg} ; \sigma = 620 \mathrm {~kg}μ=1510 kg;σ=620 kg

Suppose That the Weights of Vans Delivering Goods to Inner $\mu = 1510 \mathrm {~kg} ; \sigma = 620 \mathrm {~kg}$