Boxes of sugar are filled by machine with considerable accuracy. The distributio

Question

Boxes of sugar are filled by machine with considerable accuracy. The distribution of box weights is normal and has a mean of 33 ounces with a standard deviation of 3.6 ounces. a. What is the probability that a randomly selected box weighs more than 34.5? b. If 5 box were selected randomly and their weight obtained. What is the probability 1. that the mean of the 5 boxes is less than 29? Will this be unusual? A city currently does not have a National Football League team, 65% of all the city residents are in favor of attracting NFL team. a. A random sample 900 of the city residents is selected, and asked if they would want 2, an NFL team. Describe the sampling distribution of p, the proportion of the residents b. In the sample obtained in part a, what is the probability the proportion of residents who want NFL team is greater than 63%? c. What is the probability that 630 or fewer of the residents want the NFL team? Will 758 of 1024 randomly selected adult Ghanaians aged 18 or older stated that a candidate's positions on the issue of family values are extremely or very important in 3. a. Obtain a point estimate for the proportion of adult Ghanaians aged 18 or older who believe family values are extremely or very important in determining their vote for b. Verify the requirements for constructing a confidence interval for p are satisfied c. Construct and interpret a 99% confidence interval for the proportion of adult Ghanaians aged 18 or older who believe family values are extremely or very important in determining their vote for president. The following data represent the ages (in weeks) at which babies first crawl based ona survey of 18 mothers conducted by Essential Baby. Construct and interpret a 90% confidence interval for the mean age at which baby first crawls. 4. 47 3756 26 39 28 49 40 422529 33

Explanation / Answer

4) P(X<=10)=P(X=0)+....=P(X=10)=0.783

P(X=0)=15C0(0.6)^0(0.4)^15=0.0000, compute remaining probbailities and add the values to find the probbaility of atmost 10 successes. [Substitute probbaility of success, p=0.6, number of success, n=15 and specific number of success in n=15 trials is r=10 in P(X,r)=nCr(p)^r(q)^n-r]

5) Since Z scores are of different signs, add the area corresponding to area between z scores and mean for two z scores.

P(-2<Z<2)=0.4772+0.4772=0.9544

6) The sampling distribution is normal with mean, mu=30.8 and standard deviation, s=6.2/sqrt 40=0.98

7) The 95% c.i=Ps+-Zqrt[Ps(1-Ps)/N], where Ps is sample proportion, and N is sample size, Z corresponds to Z score at alpha=0.05.

=960/1200+-1.96sqrt[960/1200(1-960/1200)/1200]

=0.777 to 0.823

8) Reject null hypothesis.

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