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1.The waiting time, in hour, between successive speeders spotted by a radar units is a continuous random variable with cumulative distribution function
"f(x)={(1-e^(-8x), if x>0,0 otherwise)"derive the characteristic function of x and use it to find the mean of x
Solve the corresponding equation for the appropriate interval by using the following two root finding techniques :
a) algebraic approach
sin(x+ π /2)=ln|x-1|
What is the number of subsets of a set with n elements, containing a given element (when element becomes fixed, part of every subset)?
A ball is thrown vertically upward with a speed of 7.1 m/s. Find:
(9 points)
a. Maximum height reached the ball
b. Its time of flight
c. Velocity the ball would return to its starting point
How many different samples of size 8 can be selected from a population with a size of 12 ?
Let S be a subset of F3 defined as S = (x; y; z) F 3 : x+y+2z-1=0
is S a subspace of F3 or not
Determine whether the set S is subspace of R5 defined by
S = f(x1; x2; x3; x4; x5) R5
: x1 = 3x2 and x3 = 7x4:
A. Find the length of the following confidence interval.
1. Upper limit = 0.995
Lower Limit = 0.437
2. Upper limit = 394.14
Lower Limit = 354.74
3. Upper limit = 0.02946
Lower Limit = 0.02244
4. 0.475 < p < 0.735
5. 0.355 < p < 0.570
A. Find the length of the confidence interval (s = standard deviation)
1. s = 3
n = 250
Confidence level = 95%
2. s = 6
n = 400
Confidence level = 99%
B. Determine the sample size, given the following data.
1. s = 5
E = 2.42
Confidence level = 95%
2. You want to estimate the mean gasoline price within your town to the margin of error of 6 centavos. Local newspaper reports the standard deviation for gas price in the area is 30 centavos. What sample size is needed to estimate the mean gas prices at 99% confidence level?
3. Carlos wants to replicate a study where the highest observed value is 14.8 while the lowest is 14.2. He wants to estimate the population mean µ to the margin of error of 0.025 of its true value. Using 95% confidence level, find the sample size n that he need.
A consumer advocacy group suspects that a local supermarket’s 500 grams of sugar actually weigh less than 50 grams. The group look a random sample of 20 such packages, weigh each one, and found the mean weight for the sample to be 496 grams with standard deviation of 8 grams. Using 1% significance level, would you conclude that the mean weight is less than 500 grams? Also, find the 99% confidence interval of the true mean.
#339914 on Dec 2023