1)A particular fruit's weights are normally distributed, with a mean of 462 grams and a standard deviation of 31 grams.

If you pick 17 fruits at random, then 4% of the time, their mean weight will be greater than how many grams?

Give your answer to the nearest gram.

2)A population of values has a normal distribution with mean=54.2 and standard deviation=85.9 , you intend to draw a random sample of size n=127

a)Find the probability that a single randomly selected value is greater than 52.7

b)Find the probability that a simple of size n=127 is randomly selected with a mean greater than 52.7

Enter your answers as numbers accurate to four decimal places , answers obtaining using exact z-scores or z-scores rounded to three decimal places are acceptable.

3) A food marketing institute found that 47% of households spend more than $125 a week on groceries. Assume the population proportion is 0.47 and a simple random sample of 87 households is selected from the population. What is the probability that the sample proportion of households spending more than $125 a week is more than 0.4

Note: you should carefully round any z-values you calculate to 4 decimal places to match wamap's approach and calculations.

4)A population of values has a normal distribution with mean=30.8 and a standard deviation=88.9 you intend to draw a random sample of size n=244

a)Find the probability that a sample of size n=244 is randomly selected with a mean less than 34.2.

5)A population of value has a normal distribution with mean=7 and a standard deviation= 54.5 you intend to draw a random sample of size n=108

a) find the probability that a sample of size n=108 is randomly selected with a mean between -7.7 and 22.2

6)A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 179.5cm and a standard deviation of 1.3 cm. For shipment, 19 steel rods are bundled together.

a) find the probability that the average length of a randomly selected bundle of steel rods is less than 178.6 cm.

7)In 2011 the U.S Department of transportation reported with 95% confidence that the average length of a motor vehicle trip in the United States was 9.72 miles with a margin or error of 0.22 miles.

a)with 95% confidence the authors of the report are claiming that the true average length of a motor vehicle trip in the United States is between...... and .............miles

b)the level of confidence for this estimate is....

8)If n=330 and p(p-hat)=0.39 , find the margin of error at a 95% confidence level

Give your answer to three decimals