Task 1. Solve the following questions: Q1: The distribution of heights of adult
ID: 344959 • Letter: T
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Task 1. Solve the following questions: Q1: The distribution of heights of adult American men is approximately Normal with mean 69 inches and standard deviation 2.5 inches. What percent of men are taller than 74 inches? Q2. The distribution of heights of adult American men is approximately Normal with mean 69 inches and standard deviation 2.5 inches. Between what heights do the middle 95% of men fall? Q3. 5 z=1.15 is . The proportion of observations from a standard Normal distribution with values less than Q4. What is the z-score value that corresponds to the 97th percentile? Q5. The mean life of a tire is 30,000 km. The standard deviation is 2000 km. Then, 68% of all tires will have a life between km andX km. Individual Consultative (Pair) QuestionExplanation / Answer
= 69 inches
+ 1 (Std deviation) and - 1 (Std deviation) = 68% of population sample
+ 2 (Std deviation) and - 2 (Std deviation)= 95% of population sample
Answer 1 - One standard deviation, Upper limit = 69+2.5 = 71.5 inches
Two standard deviation, upper limit = 69+2*2.5 = 74 inches
Since, the height range is two standard deviations above mean, 2.5% of the population would be taller than 74 inches.
Answer 2 - 95% of men would fall in the range of two standard deviations i.e 69 + 2*2.5 And 69-2*2.5 = 64 - 74 inches
Answer 3 - 0.8749, or 87.49%. We will need to look up CDF table of normal distribution and find the value of the probability at Z =1.15
Answer 4- Z is 1.881. Please refer CDF table.
Answer 5- 68% is one standard deviation. So tire would last for , 30000 -2000 to 30000 + 2000 Km = 28000 KM to 32000 KM
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