Search & Filtering
At a local high school, GPA's are normally distributed with a mean of 2.5 and standard deviation of 0.6. What percentage of students at the high school have a GPA higher than 3.0?
At a local high school, GPA's are normally distributed with a mean of 2.5 and standard deviation of 0.6. What percentage of students at the high school have a GPA higher than 3.0?
Marks 10-19 20-29 30-39 40-49 50-59 60-69
Number of students 4 8 a 22 48 b
The mean score of the students was 46.5
(i) Show that the values of a and b are 12 and 6 respectively. (5marks)
(ii) Estimate the median for the above sample. (3marks)
(iii) Determine the variance and the standard deviation (4 marks)
(iv) Given that 32% of the students failed the examination, what was the cut off points.
(3 marks)
(v)Estimate the mode for this data. (3marks)
. In a class, 50% of the students study physics and Biology. 70% of the students study physics. What is the probability of a student studying Biology given he/she is already studying physics?
You would be introducing a new product in your company to increase the sales because the company’s sales has been declining for the past years. Initially, you would want to find out whether such product will be the preferred product by the consumers. What technique would you use and why?
The park officials of Kruger Park believe that 50% of the buffaloes in the southern part have tuber-
culosis. The characteristic being studied is the occurrence of tuberculosis. A random sample of
100 buffalo is obtained from the southern part of the Kruger Park for which 65 are tested positively
for tuberculosis.
(a) Do the data indicate that the proportion of buffalo in the southern part that have tuberculosis
is greater than assumed? Perform a proper hypothesis test and test at the 5% significance
level. Clearly show how you draw a conclusion when you test this hypothesis, using both
methods, i.e.
(i) critical value approach, and (10)
(ii) p-value approach. (3)
(b) Assume that for practical importance the park officials would be concerned if the occurrence
of tuberculosis is more than an additional 10% of the existing proportion. What practical
conclusion might they draw from the results?
[Hint: Compute a 95% lower one-sided confidence bound. (7)
A survey of the number of children in families in a small town gave the following results.
2 3 1 3 1 2 0 0 1 2 1 0 1 3 1
Does this data provide sufficient evidence that the average number of children per family is less
than 2, at the 10% significance level? Clearly show how you draw a conclusion when you test this
hypothesis. Show calculations of all statistics used.
[20]
A new manufacturing method is supposed to increase the average life span of electronic com-
ponents, while the variance of the life span is expected to stay the same. Using the previous
manufacturing method, the average life span was 110 hours with a variance of 9 hours. The manu-
facturer measures the life spans of a sample of components manufactured using the new method.
The sample of 20 yields a sample mean of 125 for the life spans of the components. Does the data
provide sufficient evidence for the claim at the 1% level of significance? Clearly show how you draw
a conclusion when you test this hypothesis, using both methods, i.e.
(a) critical value approach, and (15)
(b) p-value approach. (5)
#331389 on Nov 2022