Quiz 7

1.

Frank works for NASA designing planetary rovers. For his current project, he has to design a rover capable of withstanding the harsh climate on the surface of Venus. As part of his design work, Frank models the daily high surface temperature of Venus using a normal distribution with a mean of 

  and a standard deviation of

.

Use this table or the ALEKS calculator to find the percentage of daily high temperatures between 

  according to the model. For your intermediate computations, use four or more decimal places. Give your final answer to two decimal places (for example 98.23% ).

________

2.  Seventy million pounds of trout are grown in the U.S. every year. Farm-raised trout contain an average of 32 grams of fat per pound, with a standard deviation of 8  grams of fat per pound. A random sample of36  farm-raised trout is selected. The mean fat content for the sample is  29.7 grams per pound. Find the probability of observing a sample mean of 29.7 grams of fat per pound or less in a random sample of 36 farm-raised trout.
Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places.

________

3.  There is a very popular lottery in which a ticket is called a scratcher. In this lottery, 43% of the scratchers are winning ones. Suppose that we will take a random sample of 10 scratchers. Let

represent the proportion of winning scratchers from the sample. Consider the sampling distribution of the sample proportion

.
Complete the following. Carry your intermediate computations to four or more decimal places. Write your answers with two decimal places, rounding if needed.

Answer Submitted:
(a)Find the mean of the sampling distribution of the sample proportion.

(b)Find the standard deviation of the sampling distribution of the sample proportion).

4.   Let Z be a standard normal random variable. Use the calculator provided, or this table, to determine the value of c.

$P\left(Z\le c\right)=0.2236$

Carry your intermediate computations to at least four decimal places. Round your answer to two decimal places.

_______

5.  Joe, a highway safety inspector, is concerned about the potential for accidents caused by boulders that fall down a sandstone cliff beside a main highway. As part of an accident simulator, Joe models the boulders’ weights using a normal distribution with a mean of 563kg  and a standard deviation of  150 kg..
Use this table or the ALEKS calculator to find the percentage of boulders that weigh between 245kg   and  449kg according to the model. For your intermediate computations, use four or more decimal places. Give your final answer to two decimal places (for example 98.23%).

__________