The mean life of a tire is 35,000 miles and the standard deviation is 3,000 mile

Question

The mean life of a tire is 35,000 miles and the standard deviation is 3,000 miles. willing to replace 10% of the tires. What mileage should you include in your warranty?

Question 2: A university accepts students with ACT scores greater than 23. ACT scores are normally distributed with an average of 20.8 and a standard deviation of 4.8. A student applies to the school with an SAT score 1170 and the school is trying to decide if they should accept the student or not. The university wants to decide on a comparable cutoff for SAT scores. The average score on the SAT is 1083 with a standard deviation of 194.

What SAT score is comparable to an ACT score of 23?

Should the school accept the student?

Question 3:Consider the following letter written in to 'Dear Abby' Dear Abby: You wrote in your column that a woman is pregnant for 266 days. Who said so? I carried my baby for ten months and five days, and there is no doubt about it because I know the exact date my baby was conceived. My husband is in the Navy and it couldn't have possibly been conceived any other time because I saw him only once for an hour, and I didn't see him again until the day before the baby was born. I don't drink or run around, and there is no way this baby isn't his, so please print a retraction about the 266-day carrying time because otherwise I am in a lot of trouble. San Diego Reader This reader is claiming to have been pregnant for approximately 307 days. Pregnancy lengths give a normal distribution with an average of 268 days and a standard deviation of 14 days.

What is the probability that a pregnancy would last 307 days or longer?

What does this suggest?

Explanation / Answer

Ans:

1)

P(Z<=z)=0.1

z=-1.282

x=35000-1.282*3000=31154

So,warranty should be for 31154 miles

2)

For ACT score:

z=(23-20.8)/4.8=0.46

Comparable SAT score:

x=1083+0.46*194=1172.24

So,approximately 1172 SAT score is comparable to an ACT score of 23

3)

z=(307-268)/14=2.79

P(z>=2.79)=1-P(z<2.79)=1-0.9974=0.0026

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