Answer:
a. Left Skewed
b. More students scored above 70
c. No
d. 0.0008
e. standard deviation increases by 1.4142
Step-by-step explanation:
a. The distribution is Left skewed. The maximum possible score is 100 and the mean is 70, hence, there is a barrier preventing a long right tail.
-The scores to the left is only 20, the left therefore is longer.
-The median, 74, is higher than the mean, 70, thus the mean is more left leaning.
b.More students will score more than 70.
-the median is 74 suggesting that 50% plus have scored 74points +
- Given the mean is 70 points, it's therefore obvious that more than 50% of the students have score more than 70 points.
c. No. This is not a normal distribution therefore we cannot calculate the probability that a randomly chosen student scored above 75 using this distribution.
d. The sample size n is large, n>30, so we can use the central limit theorem to approximate the probability:
[tex]Standard \ Error=\frac{\sigma}{\sqrt{n}}\\\\=\frac{10}{\sqrt{40}}\\\\=1.5811\\\\z=\frac{75-70}{1.5811}\\\\=3.1623\\\\\\(PX>70)=P(z>3.1623)\\\\=0.0008\\[/tex]
e. The standard deviation will increase by the square root of the decreament :
[tex]\sqrt{2}=1.4142[/tex]
#Standard deviation increases by 1.4142
