Question

-The weight of an organ in adult males has a​ bell-shaped distribution with a mean of

300 grams and a standard deviation of 40 grams. Use the empirical rule to determine the following.

a. About 95% of organs will be between what​ weights?

b. What percentage of organs weighs between 260 grams and 340 ​grams?

​(c) What percentage of organs weighs less than 260 grams or more than 340 ​grams?

​(d) What percentage of organs weighs between 220 grams and 340 ​grams?

-Scores of an IQ test have a​ bell-shaped distribution with a mean of 100 and a standard deviation of 12.

Use the empirical rule to determine the following.​

(a) What percentage of people has an IQ score between 88 and 112​?

​(b) What percentage of people has an IQ score less than 88 or greater than 112​?

​(c) What percentage of people has an IQ score greater than 112

-Suppose babies born after a gestation period of 32 to 35 weeks have a mean weight of 2800 grams and a standard deviation of 800 grams while babies born after a gestation period of 40 weeks have a mean weight of 3000 grams and a standard deviation of 475 grams. If a 33​-week gestation period baby weighs 3075 grams and a 41​-week gestation period baby weighs 3275 ​grams, find the corresponding​ z-scores. Which baby weighs more relative to the gestation​ period?

-In a certain​ city, the average​ 20- to​ 29-year old man is 69.8 inches​ tall, with a standard deviation of 3.0 ​inches, while the average​ 20- to​ 29-year old woman is 64.5 inches​ tall, with a standard deviation of 3.9 inches. Who is relatively​ taller, a​ 75-inch man or a​ 70-inch woman?

-A manufacturer of bolts has a​ quality-control policy that requires it to destroy any bolts that are more than 4 standard deviations from the mean. The​ quality-control engineer knows that the bolts coming off the assembly line have mean length of 12 cm with a standard deviation of 0.05 cm. For what lengths will a bolt be​ destroyed?

Answer 1

Q 1) The weight of an organ in adult males has a​ bell-shaped distribution with a mean of

300 grams and a standard deviation of 40 grams. Use the empirical rule to determine the following.

a) About 95% of organs will be between what​ weights?

The 95% of organs will be between 220 gms and 380 gms

b) What percentage of organs weighs between 260 grams and 340 ​grams?

Answer: 68.27%

c)  What percentage of organs weighs less than 260 grams or more than 340 ​grams?

Answer: 31.74%

​(d) What percentage of organs weighs between 220 grams and 340 ​grams?

Answer: 81.85%