Normal Distribution and Probability

The Nordic Ecolabel is the official Ecolabel of the Nordic countries and was established in 1989 by the Nordic Council of Ministers.The Nordic Ecolabel evaluates a product's impact on the environment throughout the whole life cycle. The label guarantees among other things that climate requirements are taken into account, and that CO2 emissions (and other harmful gasses) are limited.The "Swan" symbol, as it is known in Nordic countries, is available for a large number of product groups. Companies can obtain the right to use the Nordic Ecolabel on their
product via a licensing process. Environmental criteria, performance criteria and quality and regulatory criteria must be satisfied.
A Nordic Ecolabelled bakery is a bakery that has been awarded a Nordic Ecolabel licence subject to strict requirements that cover the entire business. Criteria are set on ingredients, energy use, packaging, transport, cleaning chemicals, the working environment and waste management. A Nordic Ecolabelled bakery must ensure that the manufacturing of the bread has a low environmental impact from a life cycle perspective. This applies to the baking as well as the supplier chain. One of the requirements is that the total energy used in the bakery's production process should not exceed 1.50 kilowatts per hour per kg. Another is that at least 95% of the palm oil used in the bakery must be certified according to a standard that includes balancing financial, ecological and social interests and this standard must promote and contribute towards sustainable forestry agriculture.
A study of Bread Basket Bakeries, a chain of Nordic bakeries, found that the average amount of energy used in their bakeries follows a normal distribution with a mean of 2 kilowatts per hour per kg and a standard deviation of 0.75kilowatts per hour per kg. Show your working, including appropriate diagrams, to answer the questions on the following page.

a. Find the probability that a randomly selected Bread Basket Bakery would be eligible to carry the Nordic Ecolabel.
b. Find the probability that a randomly selected Bread Basket Bakery uses between 1.25 and 1.75 kilowatts of energy per hour per kg

c. Managers of Bread Basket Bakeries with energy consumption higher than the 85th percentile of the company's energy consumption distribution must attend a workshop aimed to reduce energy use. Find the amount of energy used beyond which managers are expected to attend this workshop.

d. Find the probability that a random sample of 10 Bread Basket Bakeries will have an average energy consumption that would be acceptable for Nordic Ecolabelling.

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