Search & Filtering
If P(x) =√x, show that P(x+h) - P(x) = h(√x+h + √x).
If Φ (r)= 2^r, show that Φ (r+1) =2 Φ(r).
Consider a population having a standard deviation equal to 10, we wish to estimate the
for a mean of this population with an error bound equal to 1?
ii.Suppose we take a random sample of size we have determined in part (i), if we
i.How large a random sample is needed to construct a 95.44% confidence interval
obtain a sample mean equal to 295, calculate the 95.44% confidence interval for
the population mean. What is the interval error bound?
If F(z)= log z, show that F(xy) = F(x) +F(y).
Using the methods suggested in the preceding problem, find the area of the trapezoid bounded by the line y= x+3, the ordinates x=1, x=3, and the x axis.
By use of a procedure similar to that discussed in Article 19, find the area of the triangle OAP (Figure 30) as the limit of a sum of inscribed rectangular areas. Do the same for circumscribed rectangular areas.
the mathematics teacher claims that the mean iq of statistics students is 110 with standard deviation of 12. The mean IQ of 28 randomly selected statistics students is 112 . Test the difference of the population and sample means at 5%level of significance.
A ball thrown straight up is located s feet above the ground at t seconds after it is thrown in accordance with the formula s= 112t-16 t^2. Find a formula for the velocity of the ball and find (a) the time required to reach its highest point, (b) the distance of the highest point above the ground, and (c) the acceleration of the ball at this point.
A bank Manager developed a new System to reduce the time customers spend waiting for a teller
service during peak hours. The Manager hopes that the new system will reduce the waiting time
hypothesis and alternative hypothesis needed if we want to attempt to provide evidence
the 100 waiting times to support the claim that the mean waiting time under new system is shorter
than 6 minutes.
from the current 9 to 10 minutes to less than 6 minutes. Suppose that the Managerwishes to use
a)Letting µ represent the mean waiting time under the new system, set up the null
b)In the context of this situation interpret making a type I error, interpret making a type II error
supporting claim that µ is shorter than 6 minutes.
A ball rolling down an incline travels s feet in t seconds, where s= 5t^2. Derive a formula for the velocity of the ball at time t= t0. How fast is it going (a) after 2 seconds (b) after it has rolled 80 feet?
