Central Limit Theorem

 A group of 625 students has a mean age of 15.8 years with a standard deviation of 0.6 years.  The ages are normally distributed. What is the probability that a randomly selected student is older than 16.5 years old?

• 0.864
• 0.879
• 0.121
• None of these

Tags

CCSS.HSS.ID.A.4

The mean and standard deviation of a population are 200 and 20, respectively. 
What is the probability of selecting 25 data values with a mean less than 190?

• 69%
• 0.6%
• 31%
• 99%

Tags

CCSS.HSS.ID.A.4

A soft drink bottler claims that, on average, cans contain 12 oz. of soda. Suppose the true distribution of soda volumes is normally distributed with a mean of 12 oz. and a standard deviation of .16 oz. Sixteen cans are randomly selected and their volumes are measured. What is the probability the average volume will be between 11.96 and 12.08 oz.?

• .2902
• .8186
• .7424
• .3194

Tags

CCSS.HSS.ID.A.4

The Wechsler Adult Intelligence Scale (WAIS) is a common “IQ test” for adults.  The distribution of WAIS scores for persons over 16 years of age is approximately normal with mean 100 and standard deviation 15. What is the probability that the average WAIS score of a simple random sample of 60 people is 105 or higher? 

• .9951
• .5021
• .2361
• .0049

Tags

CCSS.HSS.ID.A.4

The amount of fuel used by jumbo jets to take off is normally distributed with a mean of 4000 gallons and a standard deviation of 125 gallons.  What is the probability that the mean number of gallons of fuel needed to take off for a randomly selected sample of 40 jumbo jets will be less than 3950 gallons?

• .0057
• .025
• .345
• .781

Tags

CCSS.HSS.ID.A.4

Frequent fliers of a particular airline fly a random number of miles each year, having mean and standard deviation (in thousands of miles) of 23 and 11, respectively. The airline decides to randomly select 25 of these fliers and record the number of miles that each individual flew the past year. Compute the approximate probability that the sample mean of the miles flew will be greater than 26 thousand miles.

• .3925
• .1983
• .873
• .087

Tags

CCSS.HSS.ID.A.4

Researches found that boys playing high school football absorb an average of 355 hits to the head with a standard deviation of 80 hits during a season.  What is the probability on a randomly selected team of 48 players that the average number of head hits per player is between 340 and 360?

• .236
• .429
• .571
• .614

Tags

CCSS.HSS.ID.A.4

CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.4

CCSS.HSS.MD.A.3

Suppose the teenagers that attend public high schools get an average of 5.7 hours of sleep each night with a standard deviation of 1.7 hours.  What is the probability that a randomly selected group of 35 high school students get more than 6 hours of sleep each night?

• .430
• .148
• .281
• .087

Tags

CCSS.HSS.ID.A.4

CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.4

CCSS.HSS.MD.A.3

Engineers must consider the breadths of male heads when designing motorcycle helmets. Men have head breadths that are normally distributed with a mean of 6.0 inches and a standard deviation of 1.0 inch. 

If one male is randomly selected, find the probability that his head breadth is less than 6.2 inches.

• .6801
• .4207
• .5793
• .5101

Tags

CCSS.HSS.ID.A.4

State whether you would use the central limit theorem or the normal distribution:
The weights of the eggs produced by a certain breed of hen are normally distributed with mean 65 grams and standard deviation of 5 grams.
What is the probability that the average weight of a dozen eggs selected at random will be more than 68 grams? 

• Central Limit Theorem
• Normal Distribution

Tags

CCSS.HSS.ID.A.4