MATH 1740: Section: 91: Intro to Stat: Online Summer 18 Matilda Zoker I 7/1/18 6

Question

MATH 1740: Section: 91: Intro to Stat: Online Summer 18 Matilda Zoker I 7/1/18 6:46 PM Quiz: Chapter 6 Quiz This Question: 1 pt 45 of 14 (9 complete) This Quiz: 14 pts Help lake Based on an assumption of a mean weight of 145 Itb, the boat was rated to carry 50 passengers (so the load limit was 7,250 tb) After the boat sank, the assumed mean weight for similar boats was changed from 145 tb to 173 lb. Complete parts a and b a. Assume that a similar boat is loaded with 50 deviation of 35.8 ib. Find the probability that the boat is overloaded because the 50 passengers have a mean weight greater than 1 assengers, and assume that the weights of people are normally distributed with a mean of 1766 lb and a standard (Round to four decimal places as needed) o. The boat was later rated to carry only 17 passengers, and the koad limit was changed to 2,941 Ib. Find the probability that the boat is overloaded because the mean weight of the passengers is greater than 173 (so that their total weight is greater than the maximum The probability is Round to four decimal places as needed) Do the new ratings appear to be safe when the boat is loaded with 17 passengers? Choose the correct answer below capacity of 2 941 lb) O A. Because there is a high probability of overloading, the new ratings appear to be safe when the boat is loaded with 17 passengers O B. Because 176 6 is greater than 173, the new ratings do not appear to be sale when the boat is loaded wth 17 passengers ° C. Because the probability of overloading is lower with the new ratings than with the old ratings, the new targs appear to be safe ?D. Because there is a h probablity of overtoading, the new ratin S do n? appear to be sie when the boat is loaded wth 17 passen es Quiz Chapter 1

Explanation / Answer

a)

P(X>145)=P(Z>(145-176.6)/(35.8/sqrt(50))=P(Z>-6.24)=1.0000

b)

P(X>173)=P(Z>(173-176.6)/(35.8/sqrt(17))=P(Z>-0.41)=0.6591 ( please try 0.6608 if this comes wrong and revert)

c)

option D is correct ; because there is a high probability........

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