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The first four Hermite polynomials are f(x) = 1,g(x) = 2t, h(x) = 2−4t +t², and p(x) =
6−18t +9t²−t³
. Show that these polynomials form a basis for P3.
Let x, y and z be three vectors in a vector space V
a. Prove that the span{x,y, z} is a subspace of V.
The weights of students in a certain school are normally distributed with a mean weight of 66 kg. 10% have a weight greater than 70kg. What percentage of students weighs between 52kg and 66kg?
- A DepEd official claim that the average performance in Mathematics is 82.4%. A random of 25 students showed that their mean performance in Mathematics is 81.3% with a standard deviation of 4.2%. Test whether the mean performance of the students is not significantly lower than the general average. Use 0.01 level of significance.
Two dices are tossed together, what is the probability of having a multiple of 12.
2. In a Math test, the mean score is 45 and the standard deviation is 4. Assuming normality, what is the probability
that a score picked at random will lie
ve score 50?
b. below score 38?
a.
3.
Consider the normal distribution of IQs with a mean of 100 and a standard dev
Show that X^2 + Y^2 + Dx + Ey + F=0 represents a circle of positive radius if and only if D^2 + E^2 - 4F > 0.
n = 68, ¯x=75, and σ = 8. The sample population is normally distributed. Find the 99% interval estimate for µ.
A sample of 100 Grade 9 students’ ages have been obtained to estimate the mean age of all Grade 9 students. ¯x=16 years and the population variance is 0.75 years. Find the 95% confidence interval for µ.
The speed(v) of car in m/s is related to time t in second by the equation: v= 3+12t-3t^ . Find the maximum of the car in km/h?
