more 6 appears more than 2 times mean 10 and standard 4. 3 points) Suppose X is
ID: 3253180 • Letter: M
Question
more 6 appears more than 2 times mean 10 and standard 4. 3 points) Suppose X is a normally distributed random variable with deviation 3. Find (a) point P(X 13), (b) point) P(X 12), (c) point] P(8 X s 11), mean 100, a ran- 5. 4 points To test the hypothesis that a normally distributed population has standard dom of size 10 is chosen. Suppose the sample mean is 110 and the population deviation is known to equal 15 (a) 1 point) state alternative hypotheses that should be tested the null and (b) point] what is the z-stat for this hypothosis test? (c) point] What is the p value for this hypothesis t the null hypothesis? (d) li pointl Using the 5 nt level of significance, would you roject 6 5 points) A that the moan lifetime of tho battcrics it produces is at least 250 hours of use. You decide to conduct a t-test to verify the validly of the manufacturer's claim. A sample of 20 batteries yielded the following data: 237, 254, 255, 239, 244, 248, 252, 255, 233, 259, 236, 232, 243, 261, 255, 245, 218, 243, 238, 216. Page 2 of 3 Spring 2017Explanation / Answer
4. X~N(10,32)
a) P[X<13]=P[(X-10)/3<(13-10)/3]=P[Z<1]=0.8413447 [answer] where Z~N(0,1)
b) P[X>=12]=P[(X-10)/3>=(12-10)/3]=P[Z>=0.667]=0.2523861 [answer] where Z~N(0,1)
c) P[8<X<=11]=P[X<=11]-P[X<8]=P[(X-10)/3<(11-10)/3]-P[(X-10)/3<(8-10)/3]=P[Z<0.333]-P[Z<-0.667]=0.6304329-0.2523861= 0.3780468 [answer]
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