Answer #5 letters: a,b Answer #6 letters: a,b Answer #7 5. In Gym class, the run

Question

Answer #5 letters: a,b Answer #6 letters: a,b Answer #7
5. In Gym class, the running times for a mile are normally distributed, with a mean of 360 seconds and a standard deviation of 65 seconds. a. what time in seconds is the cutoff for the fastest 5%? b, what time in seconds is the cutoff for the slowest 25%? 6. The average calories count of a cheese burger from the fast food chain is 440 with a standard deviation of 30. You must include a graph of the distribution curve for each question. a. what amount of calories will mark the top 5% of hamburgers? b. What amount of calories will mark the 90 percentile of the hamburgers? 7. A study from the World Bank in 2015 showed that the mean life span of all American is 78.74 years with a standard deviation of 15 years while the mean life span of all Japanese is 83.84 years with a standard deviation of 18 years. Between a 90 years old American and a 95 years old Japanese, who will be considered to have a longer life comparing to their respective population? Use Z-score to justify your answer.

Explanation / Answer

5)a) P(X < x) = 0.05

or, P((X - mean)/sd < (x - 360)/65) = 0.05

or, P(Z < (x - 360)/65) = 0.05

or, (x - 360)/65 = -1.645

or, x = -1.645 * 65 + 360

or, x = 253.075

b) P(X > x) = 0.25

or, P((X - mean)//sd > (x - 360)/65) = 0.25

or, P(Z> (x - 360)/65) = 0.25

or, P(Z < (x - 360)/65) = 0.75

or, (x - 360)/65) = 0.67

or, x = 0.67 * 65 + 360

or, x = 403.55

6)a) P(X > x) = 0.05

or, P((X - mean)/sd > (x - mean)/sd) = 0.05

or, P(Z > (x - 440)/30) = 0.05

or, 1 - P(Z < (x - 440)/30) = 0.05

or, P(Z < (x - 440)/30) = 0.95

or, (x - 440)/30 = 1.645

or, x = 1.645 * 30 + 440

or, x = 489.35

b) P(X < x) = 0.9

or, P((X - mean)/sd > (x - mean)/sd) = 0.9

or, P(Z < (x - 440)/30) = 0.9

or, (x - 440)/30 = 1.28

or, x = 1.28 * 30 + 440

or, x = 478.4

7) For America

z-score = (X - mean)/sd

           = (90 - 78.74)/15

          = 0.75

For japan

z-score = (X - mean)/sd

            = (95 - 83.84)/18

            = 0.62

As the z-score forAmerican is greater than japanese, so American will be considered to have a longer life.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---