Question

What price do farmers get for their watermelon crops? In the third week of July, a random sample of 45 farming regions gave a sample mean of  = $6.88 per 100 pounds of watermelon. Assume that σ is known to be $1.92 per 100 pounds.

(a)

Find a 90% confidence interval for the population mean price (per 100 pounds) that farmers in this region get for their watermelon crop (in dollars). What is the margin of error (in dollars)? (For each answer, enter a number. Round your answers to two decimal places.)
lower limit     $  
upper limit     $  
margin of error     $  

(b)

Find the sample size necessary for a 90% confidence level with maximal error of estimate E = 0.35 for the mean price per 100 pounds of watermelon. (Enter a number. Round up to the nearest whole number.)
farming regions

(c)

A farm brings 15 tons of watermelon to market. Find a 90% confidence interval for the population mean cash value of this crop (in dollars). What is the margin of error (in dollars)? Hint: 1 ton is 2000 pounds. (For each answer, enter a number. Round your answers to two decimal places.)
lower limit     $  
upper limit     $  
margin of error     $

2. Suppose x has a distribution with a mean of 70 and a standard deviation of 27. Random samples of size  n = 36 are drawn.

(a)

Describe the   distribution.

has a geometric distribution. has a Poisson distribution.      has a normal distribution. has an approximately normal distribution. has an unknown distribution. has a binomial distribution.

Compute the mean and standard deviation of the distribution. (For each answer, enter a number.)

= mu sub x bar =

= sigma sub x bar =

(b)

Find the z value corresponding to   = 61. (Enter an exact number.)
z =  

(c)

Find  P( < 61). (Enter a number. Round your answer to four decimal places.)
P( < 61) = P(x bar < 61)

(d)

Would it be unusual for a random sample of size 36 from the x distribution to have a sample mean less than 61? Explain.

Yes, it would be unusual because more than 5% of all such samples have means less than 61.Yes, it would be unusual because less than 5% of all such samples have means less than 61.     No, it would not be unusual because less than 5% of all such samples have means less than 61.No, it would not be unusual because more than 5% of all such samples have means less than 61.

Answer 1