Question

1)

Assume that the national average score on a standardized test is 1010, and the standard deviation is 200, where scores are normally distributed. What is the probability that a test taker scores at least 1600 on the test?

• Round your answer to two decimal places.

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2)

Assume that the salaries of elementary school teachers in a particular country are normally distributed with a mean of $38,000 and a standard deviation of $4,000. What is the cutoff salary for teachers in the top 7%?

• Use Excel, and round your answer to the nearest dollar.

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3) A cookie manufacturer sells boxes of cookies that claim to weigh 16 ounces on the packaging. Due to variation in the manufacturing process, the weight of the manufactured boxes follows a normal distribution with a mean of 16 ounces and a standard deviation of 0.25 ounce. The manufacturer decides it does not want to sell any boxes with weights below the 1st percentile so as to avoid negative customer responses. What is the minimum acceptable weight, in ounces, of a box of cookies? Round your answer to two decimal places.

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4) The weights of bags of raisins are normally distributed with a mean of 175 grams and a standard deviation of 10 grams. Bags in the upper 4.5% are too heavy and must be repackaged. Also, bags in the lower 5% do not meet the minimum weight requirement and must be repackaged. What are the ranges of weights for raisin bags that need to be repackaged? Use a TI-83, TI-83 plus, or TI-84 calculator, and round your answers to the nearest integer.

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5)

The resistance of a strain gauge is normally distributed with a mean of 100 ohms and a standard deviation of 0.3 ohms. To meet the specification, the resistance must be within the range 100±0.7 ohms. What proportion of gauges is acceptable?

• Round your answer to four decimal places.

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6)

Suppose that the weight of sweet cherries is normally distributed with mean μ=6 ounces and standard deviation σ=1.4 ounces. What proportion of sweet cherries weigh more than 4.7 ounces?

• Round your answer to four decimal places.

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7)

Suppose X∼N(8,1.5), and x=5. Find and interpret the z-score of the standardized normal random variable.

The z-score when x=5 is ___. The mean is ____

This z-score tells you that x=5 is ___ standard deviations to the left of the mean.

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Answer 1

1)

Assume that the national average score on a standardized test is 1010, and the standard deviation is 200, where scores are normally distributed. What is the probability that a test taker scores at least 1600 on the test?

Answer)

As the data is normally distributed we can use standard normal z table to estimate the answers

Z = (x-mean)/s.d

Given mean = 1010

S.d = 200

We need to find

P(x>1600)

Z = (1600-1010)/200 = 2.95

From z table

P(z>2.95) = 0.0016

2)

2)

Assume that the salaries of elementary school teachers in a particular country are normally distributed with a mean of $38,000 and a standard deviation of $4,000. What is the cutoff salary for teachers in the top 7%?

Answer)

As the data is normally distributed we can use standard normal z table to estimate the answers

Z = (x-mean)/s.d

Given mean = 38000

S.d = 4000

From z table, P(z>1.48) = 7%

So, 1.48 = (x - 38000)/4000

X = 43920