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An association of City Mayors conducted a study to determine the average number of times a family went to buy necessities in a week. They found that the mean is 4 times in a week. A random sample of 25 families were asked and found a mean of 5 times in a week and a standard deviation of 2. Use 1% significance level to test that the population mean is greater than 4 hours. Assume that the population is normally distributed.
Two different moulds grow at different rates. The mass of the first mould (in grams) is well described by the function m1(t) = 20 log(t + 2) where the time t is measured in hours. The second mould grows according to m2(t) = t 2 . Question 3 continues on the next page.
(a) Write a MATLAB program using array operations to generate a table (with headings) of the amount of each mould each hour starting at time t = 0 up to a maximum time entered by the user. Run your program with the maximum time set to 10.
(b) Write a separate MATLAB program using the plot command to graph the amount of the two moulds on the same axes for 0 ≤ t ≤ 10. Make sure you label your axes.
(c) Use the graphical output from your MATLAB program in part (b) and the ginput command to estimate the time when the amounts of the moulds are equal.
A hypothetical video game console, the Mintendo Octal 32, uses an unconventional floating point format. Floats are expressed in base 8 in the form ±0.d1d2 . . . d8 × 8 x , using one bit for the sign, 24 bits for the mantissa (expressed in binary), one bit for the sign of the exponent x, and 6 bits for the absolute value of the exponent (in binary).
(a) If the bits are stored in the order: sign, sign of exponent, exponent, mantissa, and 0 corresponds to a positive sign, then calculate the decimal representation of the number stored as 1 0 000110 010 001 000 000 000 000 000 000
(b) What is the largest real number that can be stored in the Mintendo?
An association of City Mayors conducted a study to determine the average number of times a family went to buy necessities in a week. They found that the mean is 4 times in a week. A random sample of 20 families were asked and found a mean of 5 times in a week and a standard deviation of 2. Use 5% significance level to test that the population mean is not equal to 5. Assume that the population is normally distributed. What should be the decision for the hypothesis?
Given the standardized normal distribution (with a mean of 0 and a standard deviation of 1, as in Table E.2). What is the probability that Z is greater than 1.08?
A soda manufacturer is interested in determining wheter its bottling machine tends to overfill. Each bottle is supposed to contain 12 ounces of fluid. A random sample of 25 bottles was taken and found that the mean amount of soda of the sample of bottles is 12.2 ounces with a standard deviation of 0.4 ounces. If the manufacturer decides on a significance level of 0.05 test, should the null hypothesis (u=12 ounces) be rejected?
Show that if 5/3< 2x< 11/3, then x∈{y∈R such that |y- 4/3| < 1/2}
Draw the graph of the function f, defined by f(x)= |x- 6| + |5 - x| ; x∈ [2,8]
If (an) is convergent then "\\sum_{i=1}^{\\infty} a_n" is also convergent. True or false with the full explanation.
The sum of two discontinuous function is always discontinuous function. True or false with full explanation
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