(ANSWER) MATH 225N WEEK 5 ASSIGNMENT: EVALUATING PROBABILITY USING THE NORMAL DISTRIBUTION - Essay Prowess
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# (ANSWER) MATH 225N WEEK 5 ASSIGNMENT: EVALUATING PROBABILITY USING THE NORMAL DISTRIBUTION

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1 ) Henry has collected data to find that the typing speeds for the students in a typing class has a normal distribution. What is the probability that a randomly selected student has a typing speed of less than 51 words per minute if the mean (μ) is 47 words per minute and the standard deviation (σ) is 4 words per minute? Use the empirical rule.

• Provide the final answer as a percent.

2)

Find the area to the right of the z-score 0.23 under the standard normal curve.

z0.30.20.10.00.000.38210.42070.46020.50000.010.37830.41680.45620.50400.020.37450.41290.45220.50800.030.37070.40900.44830.51200.040.36690.40520.44430.51600.050.36320.40130.44040.51990.060.35940.39740.43640.52390.070.35570.39360.43250.52790.080.35200.38970.42860.53190.090.34830.38590.42470.5359

Use the value(s) from the table above.

3)

## Question

Find the area under the standard normal curve between the z-scores 0.97 and 1.26. Do not round your answer.

z0.80.91.01.11.21.31.41.50.000.78810.81590.84130.86430.88490.90320.91920.93320.010.79100.81860.84380.86650.88690.90490.92070.93450.020.79390.82120.84610.86860.88880.90660.92220.93570.030.79670.82380.84850.87080.89070.90820.92360.93700.040.79950.82640.85080.87290.89250.90990.92510.93820.050.80230.82890.85310.87490.89440.91150.92650.93940.060.80510.83150.85540.87700.89620.91310.92790.94060.070.80780.83400.85770.87900.89800.91470.92920.94180.080.81060.83650.85990.88100.89970.91620.93060.94290.090.81330.83890.86210.88300.90150.91770.93190.9441

Use the value(s) from the table above.

4)

## Question

After collecting the data, Peter finds that the standardized test scores of the students in a school are normally distributed with mean (μ85 points and standard deviation (σ3 points. Use the Empirical Rule to find the probability that a randomly selected student’s score is greater than 76 points. Provide the final answer as a percent rounded to two decimal places.

Question 5

## Question

After collecting the data, Tammy finds that the total snowfall per year in Linndale is normally distributed with mean (μ99 inches and standard deviation (σ13 inches. What is the probability that in a randomly selected year, the snowfall was greater than 112 inches? Use the empirical rule.

• Provide the final answer as a percent.

question 6

The times to complete an obstacle course is normally distributed with mean (μ87 seconds and standard deviation (σ7 seconds. What is the probability that a randomly selected finishing time is greater than 80 seconds? Use the empirical rule

• Provide the final answer as a percent.

Question 7

## Question

Find the area to the right of the z-score 1.39 and to the left of the z-score 1.53 under the standard normal curve.

z1.21.31.41.51.61.70.000.88490.90320.91920.93320.94520.95540.010.88690.90490.92070.93450.94630.95640.020.88880.90660.92220.93570.94740.95730.030.89070.90820.92360.93700.94840.95820.040.89250.90990.92510.93820.94950.95910.050.89440.91150.92650.93940.95050.95990.060.89620.91310.92790.94060.95150.96080.070.89800.91470.92920.94180.95250.96160.080.89970.91620.93060.94290.95350.96250.090.90150.91770.93190.94410.95450.9633

Use the value(s) from the table above.

Question 8

Determine the area under the standard normal curve that lies to the right of the z-score 0.97 and to the left of the z-score 0.59.

z1.21.11.00.90.80.70.60.50.40.30.000.11510.13570.15870.18410.21190.24200.27430.30850.34460.38210.010.11310.13350.15620.18140.20900.23890.27090.30500.34090.37830.020.11120.13140.15390.17880.20610.23580.26760.30150.33720.37450.030.10930.12920.15150.17620.20330.23270.26430.29810.33360.37070.040.10750.12710.14920.17360.20050.22960.26110.29460.33000.36690.050.10560.12510.14690.17110.19770.22660.25780.29120.32640.36320.060.10380.12300.14460.16850.19490.22360.25460.28770.32280.35940.070.10200.12100.14230.16600.19220.22060.25140.28430.31920.35570.080.10030.11900.14010.16350.18940.21770.24830.28100.31560.35200.090.09850.11700.13790.16110.18670.21480.24510.27760.31210.3483

Use the value(s) from the table above.

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