Question

21. In a survey of women in a certain country​ (ages 20−​29), the mean height was 65.8 inches with a standard deviation of 2.87 inches. Answer the following questions about the specified normal distribution.

​(a) The height that represents the 95th percentile is ___.

(b) What height represents the first​ quartile?

22. The weights of bags of baby carrots are normally​ distributed, with a mean of 34 ounces and a standard deviation of 0.31 ounce. Bags in the upper​ 4.5% are too heavy and must be repackaged. What is the most a bag of baby carrots can weigh and not need to be​ repackaged?

A bag of baby carrots can weigh at most ___ ounces without needing to be repackaged.

23. A mechanic sells a brand of automobile tire that has a life expectancy that is normally​ distributed, with a mean life of 35,000 miles and a standard deviation of 2800 miles. He wants to give a guarantee for free replacement of tires that​ don't wear well. How should he word his guarantee if he is willing to replace approximately​ 10% of the​ tires?

Tires that wear out by __ miles will be replaced free of charge.

24. A vending machine dispenses coffee into a sixteen​-ounce cup. The amount of coffee dispensed into the cup is normally distributed with a standard deviation of 0.07 ounce. You can allow the cup to overfill 3​% of the time. What amount should you set as the mean amount of coffee to be​ dispensed?

___ ounces.

25. In a large section of a statistics​ class, the points for the final exam are normally​ distributed, with a mean of 74 and a standard deviation of 8. Grades are assigned such that the top​ 10% receive​ A's, the next​ 20% received​ B's, the middle​40% receive​ C's, the next​ 20% receive​ D's, and the bottom​ 10% receive​ F's. Find the lowest score on the final exam that would qualify a student for an​ A, a​ B, a​ C, and a D.

The lowest score that would qualify a student for an A is ___.

Answer 1