A The number of girls in a family B The colour of hair C The gender of a person D The length of a string E The number of students in a class. 1.Indicate, by using the letters A, B, C, D and E, which of the variables in the box above belong to EACH of the categories below. You may use each letter more than once. a) Quantitative b) Qualitative c) Discrete d) Continuous e) Nominal f) Ratio 2.The following table shows the time taken for 40 students to complete an examination Time Frequency 15-17 5 18-20 7 21-23 15 24-26 10 27-29 3 Calculate a) The mode b) The median 3. Two events A and B are such that ?(?) = 0.6,?(?) = 0.4 ??? ?(?|?) = 0.2 Find a) ?(? ∩ ?) b) ?(? ∪ ?) c) (?(?|?) d) State, with a reason, whether the events A and B are independent. 4. To get to school, a student may walk, drive or travel by bus. Twenty per cent of the students walk, 30% drive and 50% travel by bus. The probability that a student who walks will be late is 0.4 and a student who drives or travels by bus will be late is 0.20 and 0.35 respectively. a) Draw a tree diagram to illustrate this information showing the probability on EACH branch. Calculate the probability that b) a student chosen at random will arrive late c) a student traveled by bus given that they arrived late. 5. If Z ~ N(0,1) with P(Z < a) = 0.7 and P(Z
A The number of girls in a family
B The colour of hair
C The gender of a person
D The length of a string
E The number of students in a class.
1.Indicate, by using the letters A, B, C, D and E, which of the variables in the box above
belong to EACH of the categories below. You may use each letter more than once.
a) Quantitative
b) Qualitative
c) Discrete
d) Continuous
e) Nominal
f) Ratio
2.The following table shows the time taken for 40 students to complete an examination
| Time | Frequency |
| 15-17 | 5 |
| 18-20 | 7 |
| 21-23 | 15 |
| 24-26 | 10 |
| 27-29 | 3 |
Calculate
a) The
b) The
3. Two
Find
a) ?(? ∩ ?)
b) ?(? ∪ ?)
c) (?(?|?)
d) State, with a reason, whether the events A and B are independent.
4. To get to school, a student may walk, drive or travel by bus. Twenty per cent of the students
walk, 30% drive and 50% travel by bus. The probability that a student who walks
will be late is 0.4 and a student who drives or travels by bus will be late is 0.20 and 0.35
respectively.
a) Draw a tree diagram to illustrate this information showing the probability on EACH branch.
Calculate the probability that
b) a student chosen at random will arrive late
c) a student traveled by bus given that they arrived late.
5. If Z ~ N(0,1) with P(Z < a) = 0.7 and P(Z <b) = 0.8122.
a. Find P(a < Z <b)
b. Find the value of b
6. The manufacturers of a new model of car state that, when travelling at 56 miles per hour,
the petrol consumption has a mean value of 32.4 miles per gallon with a standard
deviation of 1.4 miles per gallon. Assuming a
a) calculate the probability that a randomly chosen car of that model will have a petrol
consumption greater than 30 miles per gallon when travelling at 56 miles per hour.
b) Using JASP to verify the probability in part a) above.
7. The weight of boxes of stationary from a random sample of 50 boxes had a sample mean
of 88g and a standard deviation of 9g.
a) Calculate a 97% confidence interval for the weight of all such boxes.
b) Test at the 5% level to determine whether the mean weight of all boxes is more than 87
grams.
c) Use JASP to verify your answer in a) above.
8. From a sample of 200 bread rolls from Ideal bakery, 95 of the were wheat. The manager
of the bakery claims that 49% of their rolls are wheat.
a) Calculate the 95% confidence interval for the proportion of wheat rolls.
b) Test at the 1% significance level to determine whether the true proportion is less than 49%.
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