Deciphering Problems Practice! - stats

Normal Distribution (6.2)

A report stated that the average number of times a cat returns to its food bowl during the day is 36. Assuming the variable is normally distributed with a standard deviation of 5, what is the probability that cat would return to its dish between 32 and 38 times?

Central Limit Theorem

A survey found that the average time per weekday Americans spend checking their email is 5.4 hours. Assume the variable is approximately normally distributed and the standard deviation is 1.8 hours. If a random sample of 32 people is selected, find the probability that the mean of the sample will be between 5.1 hours and 5.3 hours.

Binomial Distribution (6.4)

According to the World Almanac, 72% of households own smartphones. If a random sample of 180 households is selected, what is the probability that more than 115 but fewer than 125 have a smartphone?

Normal Distribution (6.2)

For a certain group of individuals, the average heart rate is 72 beats per minute. Assume the variable is normally distributed and the standard deviation is 3 beats per minute. If a subject is selected at random, find the probability that the person has a heart rate less than 75 beats per minute.

Central Limit Theorem (6.3)

The average lifetime of smoke detectors that a company manufactures is 5 years, or 60 months, and the standard deviation is 8 months. Find the probability that a random sample of 30 smoke detectors will have a mean lifetime between 58 and 63 months.

Binomial Distribution (6.4)

Of all 3-5 year old children, 56% are enrolled in school. If a sample of 500 such children is randomly selected, find the probability that at least 250 will be enrolled in school.

A recent study of 44 motorcycles found that the average noise pollution in decibels is 90. If the population standard deviation is 4.2 decibels, find the 90% confidence interval for the mean.

(7.2) x̄ ± z* σ/√n ; population standard deviation is known; using x̄ for mean

A pizza shop owner wishes to find the 95% confidence interval of the true mean cost of a large cheese pizza. How large should the sample be if she wishes to be accurate to within 0.15? A previous study showed that the standard deviation of the price was 0.26.

(7.2) n = ( z α / 2 σ E ) ^2; “within” “how large a sample”

A survey of 260 postgraduate students found that 52 said that they have inflated their job skills on their resumes. Estimate the true proportion of post-graduate students who have inflated their job skills on their resumes at the 95% confidence level.

(7.4) p± z α / 2 √pq/n ; “proportion" ; not given a mean;

A recent study indicated that 29% of the 100 women over age 55 in the study were widows. How large a sample must you take to be 90% confident that the estimate is within 0.05 of the true proportion of women over 55 who are widows?

(7.4) “how large a sample” “proportion” “within” ; solving for n

“proportion” indicates…

p and q values (with hats)

“within” indicates…

error or E value

when the POPULATION standard deviation is unknown you use…

t distribution table

A survey of 15 randomly selected employed people in Washington DC, found that the mean monthly income was 5050. The standard deviation for the sample is 843. Find the 99% confidence interval for the mean monthly income of the workers in Washington DC.

(7.3) “standard deviation for the SAMPLE” pop. SD unknown USE S instead of sigma; using t distribution; DEGREES OF FREEDOM