I need some assistance solving these problems. Please provide work so I can understand.
length of times that light bulbs manufactured by the Acme Corporation last is normally distributed with mean 300 days and standard deviation of 50 days.
1. What is the probability that an Acme light bulb will last less than 365 days? Do these steps.
a. Sketch a suitable normal curve, shading the area corresponding to the question
b. Calculate the z-score that corresponds to 365 days. Write the answer two ways: rounded to two places, and rounded to 4 places.
c. Use the two-place z score and Table A to answer the question.
d. Use the four-place z score and the "normal calculator" in StatCrunch to answer the question.
2. What proportion of the bulbs last more than 160 days?
3. What proportion last between 160 days and 365 days?
4. Verbal SAT scores for a particular college have a mean of 501 and a standard deviation of 111.
a. Sam refuses to tell you his SAT score, but he will tell you that he outscored 39.36% of the people at the college. What was Sam's SAT score? Solve by following these steps.
i. John says he can find Sam's z score by looking in Table A. So he looks for a z score that would give a proportion of 0.3936. (See the figure.) What z score gives this proportion?
ii. Betty says that now we know the z score, we can calculate the SAT score. Do the necessary calculation.
b. Repeat exercise 4a., but for Sue. Sue reports that her SAT was in the 76th percentile, which means she scored better than 76% of the people.
a. Find the z score (you may not find 0.7600 in the table - so find the closest number you can)
b. Use the z score to calculate the SAT.
c. If only 8% of the students scored better than Mary, what was Mary's score?
Question 4(i) graph
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