Normal Distribution and Data
S1 Jan 2001
1) The students in a class were each asked to write down how many CDs they owned. The student with the least number of CDs had 14 and all but one of the others owned 60 or fewer. The remaining student owned 65. The quartiles for the class were 30, 34 and 42 respectively.
Outliers are defined to be any values outside the limits of 1.5(Q3 – Q1) below the lower quartile or above the upper quartile.
On graph paper draw a box plot to represent these data, indicating clearly any outliers. (7) Jan 2001
2) The random variable X is normally distributed with mean 177.0 and standard deviation 6.4.
(a) Find P(166 < X < 185). (4)
It is suggested that X might be a suitable random variable to model the height, in cm, of adult males.
(b) Give two reasons why this is a sensible suggestion. (2)
(c) Explain briefly why mathematical models can help to improve our understanding of real-world problems. (2) Jan 2001
3) A fair six-sided die is rolled. The random variable Y represents the score on the uppermost, face.
(a) Write down the probability function of Y. (b) State the name of the distribution of Y. (2) (1)
Find the value of
(c) E(6Y + 2), (d) Var(4Y – 2). (4) (5) Jan 2001
| Live close | Live some distance away | Management | 6 | 14 | Administration | 25 | 10 | Production | 45 | 25 |
4) The employees of a company are classified as management, administration or production. The following table shows
1) The students in a class were each asked to write down how many CDs they owned. The student with the least number of CDs had 14 and all but one of the others owned 60 or fewer. The remaining student owned 65. The quartiles for the class were 30, 34 and 42 respectively.
Outliers are defined to be any values outside the limits of 1.5(Q3 – Q1) below the lower quartile or above the upper quartile.
On graph paper draw a box plot to represent these data, indicating clearly any outliers. (7) Jan 2001
2) The random variable X is normally distributed with mean 177.0 and standard deviation 6.4.
(a) Find P(166 < X < 185). (4)
It is suggested that X might be a suitable random variable to model the height, in cm, of adult males.
(b) Give two reasons why this is a sensible suggestion. (2)
(c) Explain briefly why mathematical models can help to improve our understanding of real-world problems. (2) Jan 2001
3) A fair six-sided die is rolled. The random variable Y represents the score on the uppermost, face.
(a) Write down the probability function of Y. (b) State the name of the distribution of Y. (2) (1)
Find the value of
(c) E(6Y + 2), (d) Var(4Y – 2). (4) (5) Jan 2001
| Live close | Live some distance away | Management | 6 | 14 | Administration | 25 | 10 | Production | 45 | 25 |
4) The employees of a company are classified as management, administration or production. The following table shows