Answer:
a) No. It is not normal.
b) The probability that 700 randomly selected cars at this freeway entrance will carry more than 1075 people is 0.104
Step-by-step explanation:
<u>(a) Could the exact distribution of the count be Normal?</u>
The exact distribution of the number of people in each car entering a freeway at a suburban interchange is not normal. Because the count is <em>discrete </em>and <em>can assume values bigger or equal to one</em>.
<u>(b) The probability that 700 randomly selected cars at this freeway entrance will carry more than 1075 people.</u>
The probability we seek is the cars carrying people with mean more than
That is P(z>z*) where z* is the z-score of 1.5357.
z* can be calculated using the equation:
z*= where
- X is the mean value wee seek for its z-score (1.5357)
- M is the average count of people entering a freeway at a suburban interchange. (1.5)
- s is the standard deviation of the count (0.75)
- N is the sample size (700)
Thus z*= ≈ 1.26
We have P(z>1.26)=1-P(z≤1.26)= 1-0.896 = 0.104