Question

1. What price do farmers get for their watermelon crops? In the third week of July, a random sample of 41 farming regions gave a sample mean of  = $6.88per 100 pounds of watermelon. Assume that σ is known to be $1.98 per 100 pounds.

1(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     $ ______

1(b) Find the sample size necessary for a 90% confidence level with maximal error of estimate E = 0.45 for the mean price per 100 pounds of watermelon. (Enter a number. Round up to the nearest whole number.)
________ farming regions

1(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. Find the mean, median, and mode of the data set.

• 9   2   8   2   7

mean____ (Enter a number.)  
median _____(Enter an exact number.)  
mode ____(Enter an exact number.)  

3. Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Enter a number. Round your answer to four decimal places.)

μ = 4; σ = 2

P(3 ≤ x ≤ 7) =_______

4. Sketch the area under the standard normal curve over the indicated interval and find the specified area. (Enter a number. Round your answer to four decimal places.)

The area to the left of z = 0.53 is ______

Answer 1

All the answers are highlighted in red.

Refer Standard normal table/Z-table or use excel function "=NORM.S.INV((1-0.05))" to find the Z-value.

Round the value to the nearest whole number.

Refer Standard normal table/Z-table or use excel function "=NORM.S.INV((1-0.05))" to find the Z-value.

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The Median is the middle number in the set of ordered data.

Sort the data in ascending order

The mode is the number that occurs more often.

Sort the data in ascending order

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Refer Standard normal table/Z-table to find the probability OR use excel formula "=NORM.S.DIST(1.5, TRUE)" & "=NORM.S.DIST(-0.5, TRUE)" to find the probability.

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Refer Standard normal table/Z-table to find the probability OR use excel formula "=NORM.S.DIST(0.53, TRUE)" to find the probability.