Suppose that the temperature is normally distributed with expectation 50o C and variance 4o C . What is the probability that the temperature T will be between 48o C and 53o C ?
What is the probability that T ≥ 52o C ?
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Find the equation of the plane passing through (2,3, −1) and perpendicular to the line joining the points (3, 4, −1) and (2, −1, 5) .
A particle is acted on by constant forces = −3i + 2 j + 5k and 2i + j −3k and is displaced from the point (2, −1, −3) to the point (4, −3, 7) . Find the total work done by the forces.
Determine the value of the constant a if the function f (x) defined below is continuous at x = 2.
From 7 men and 4 women a committee of 6 is to be formed. In how many ways can this be done (i) when the committee contains exactly 2 women, (ii) at least 2 women?
In Bengal, 30% of the population has a certain blood type. What is the probability that exactly four out of a randomly selected group of 10 Bengalis will have that blood type?
Four groups of students were subjected to different teaching techniques and tested at the end of a specified period of time. As a result of dropouts from the experimental groups the number of students varied from group to group. Do the data shown below present sufficient
evidence to indicate a difference in the mean achievement for the four teaching techniques at 0.01 level of significance? What is the conclusion if you fix the level of significance at 0.05?
| Group 1 | Group 2 | Group 3 | Group 4 |
| 65 | 75 | 59 | 94 |
| 87 | 69 | 78 | 89 |
| 73 | 83 | 67 | 80 |
| 79 | 81 | 62 | 88 |
| 81 | 72 | 83 |
|
| 69 | 79 | 76 |
|
|
| 90 |
|
|
For what values of m will the equation
x 2 − 2x (1 + 3m) + 7 (3 + 2m) = 0
have equal roots?