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What percentage of the widget weights lie

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Reference no: EM132857657

1) The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 46 ounces and a standard deviation of 8 ounces.

Use the Standard Deviation Rule, also known as the Empirical Rule.

Suggestion: sketch the distribution in order to answer these questions.

a) 99.7% of the widget weights lie between what oz and oz

b) What percentage of the widget weights lie between 30 and 70 ounces?

c) What percentage of the widget weights lie above 38 ?

2) On a planet far far away from Earth, IQ of the ruling species is normally distributed with a mean of 103 and a standard deviation of 14. Suppose one individual is randomly chosen. Let X = IQ of an individual. Round all your answers to 2 decimal places if necessary.

a. What is the distribution of X? X ~ N(,)

b. Find the probability that a randomly selected person's IQ is over 106.

c. A school offers special services for all children in the bottom 4% for IQ scores. What is the highest IQ score a child can have and still receive special services?

d. Find the Inter Quartile Range (IQR) for IQ scores.

Q1:
Q3:
IQR:

3) The weights for newborn babies is approximately normally distributed with a mean of 5.3 pounds and a standard deviation of 1.7 pounds.

Consider a group of 1000 newborn babies:

1. How many would you expect to weigh between 3 and 8 pounds?

2. How many would you expect to weigh less than 5 pounds?

3. How many would you expect to weigh more than 4 pounds?

4. How many would you expect to weigh between 5.3 and 9 pounds?

4) The combined SAT scores for the students at a local high school are normally distributed with a mean of 842 and a standard deviation of 164. The local college requires a minimum SAT score of 875 before students are considered for admision.

What percentage of students from this school have SAT scores that do not satisfy the local college's admission requirement? Enter your answer as a percent accurate to 2 decimal places.

5) Adult female height is normally distributed with a mean of 65.3 inches and a standard deviation of 2.34 inches. If an adult female is randomly selected, what is the probability that the adult female has a height greater than 68.7 inches? Round your final answer to four decimal places.

6) Adult male height is normally distributed with a mean of 68.8 inches and a standard deviation of 2.32 inches. If an adult male is randomly selected, what is the probability that the adult male has a height between 65.1 and 68.9 inches? Round your final answer to four decimal places.

7) Adult male height is normally distributed with a mean of 68.8 inches and a standard deviation of 2.32 inches. If an adult male is randomly selected, what is the probability that the adult male has a height between 65.1 and 68.9 inches? Round your final answer to four decimal places.

8) A particular fruit's weights are normally distributed, with a mean of 299 grams and a standard deviation of 27 grams.

If you pick 8 fruits at random, then 7% of the time, their mean weight will be greater than how many grams?

Give your answer to the nearest gram.

9) A manufacturer knows that their items have a lengths that are skewed right, with a mean of 15.8 inches, and standard deviation of 2.6 inches.

If 47 items are chosen at random, what is the probability that their mean length is greater than 15.6 inches?

(Round answer to four decimal places)

10) The lengths of pregnancies in a small rural village are normally distributed with a mean of 260 days and a standard deviation of 14 days.

In what range would you expect to find the middle 98% of most pregnancies?

Between _____ and ______

If you were to draw samples of size 54 from this population, in what range would you expect to find the middle 98% of most averages for the lengths of pregnancies in the sample?

Between ____ and ____

11) A manufacturer knows that their items have a normally distributed lifespan, with a mean of 2.1 years, and standard deviation of 0.7 years.

If 23 items are picked at random, 7% of the time their mean life will be less than how many years?

Give your answer to one decimal place.

Reference no: EM132857657

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