14.) Over 350 students took a college calculus final exam. The scores of the stu

Question

14.) Over 350 students took a college calculus final exam. The scores of the students follow a normal distribution. Using the information given below, determine the mean and the standard deviation for the students' scores. Give your answers to nearest tenth of a percent.
- 32% of the students scored either less than 63.3% or more than 85.9%.
- Only the top 2.5% of students scored higher than a 97%on the exam.
Mean:_______________________ Standard Deviation:____________________________

15.) Alexander, a meteorologist, is studying the daily high temperatures over the past 50 years during the month of July for the cities of Chicago and Phoenix (a sample size of 1550 July days for each city). Alexander found that in Chicago, the middle 95% of July days have a high temperature between 70°F and 98°F, while in Phoenix, the middle of 95% of July days have a high temperature between 94°F and 110°F. One particular July day, the temperature in Phoenix is exactly 17°F higher than the temperature in Chicago. Which of the following is not a valid pair of z-scores for the two cities? Circle the answer.

Chicago: z= 1.7143 Chicago: z= 0.8571
Phoenix: z= -3.2500 Phoenix: z= -1.2500

Chicago: z= 0.4286 Chicago: z= 1.5714
Phoenix: z= 0.7500 Phoenix: z=2.5000

16.) A polling company defines a "likely voter" as someone who has voted in each of the previous two elections. The company asks 815 likely voters which candidate they support in the upcoming election. Find the margin of error for the poll to the nearest tenth of a percent.

Please answer all the answers and include the steps. Your help is greatly appreciated. Thank you.

14. over 350 students took a college calculus final exam. The scores of the students follow a normal distribution. Using the information given below, determine the mean and the standard deviation for the students' scores. Give your answers to the nearest tenth of a percent 32% of the students scored either less than 63.3% or more than 85.9%. Only the top 2.5% of students scored higher than a 97% on the exam. Mean: Standard Deviation: 15. Alexander, a meteorologist, is studying the daily high temperatures over the past 50 years during the month of July for the cities of Chicago and Phoenix (a sample size of 1550 July days for each city). Alexander found that in Chicago, the middle 95% of July days have a high temperature between 70 F and 98° F, while in Phoenix, the middle 95% of July days have a high temperature between 940 F and 110° F. On one particular July day, the temperature in Phoenix is exactly 17o F higher than the temperature in Chicago. Which of the following is not a valid pair of z-scores for the two cities? Circle your answer. Chicago: 1.7143 Phoenix: 3.2500 Phoenix: 1.2500 Chicago: z 0.4286 Phoenix: 0.7500 Phoenix: 2.5000 6. A polling company defines a "likely v as someone who has voted in each of the previous two elections. The company asks 815 likely voters which candidate they support in the upcoming election. Find the margin of error for the poll to the nearest tenth of a percent

Explanation / Answer

14.) Let say maximum marks to be obtained in the exam was 100.

So, 32% of the students scored either less than 63.3 or more than 85.9

P(63.3 < X < 85.9) = 0.32

Z = 0.468 for P = 0.32

(85.9 - µ) - (63.3 - µ) = 0.468

85.9 - µ - 63.6 + µ = 0.468

85.9 - 63.3 = 0.468

= 48.2

P(X > 97) = 0.025

Z = -1.96 for P(X > 97) = 0.025

(97 - µ) / = -1.96

97 - µ = -1.96*48.2

µ = 97 + 94.47 = 191.47

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