Normal Distributions Mixed Practice

When John commutes to work, the amount of time it takes him to arrive is normally distributed with a mean of 50 minutes and a standard deviation of 4.5 minutes. Out of the 232 days that John commutes to work per year, how many times would his commute be between 52 and 56 minutes, to the nearest whole number?

(a)  

At a customer service call center for a large company, the number of calls received per hour is normally distributed with a mean of 120 calls and a standard deviation of 20 calls. What is the probability that during a given hour of the day there will be more than 82 calls, to the nearest thousandth?

(a)  

IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. What is the probability that a randomly chosen person's IQ score will be less than 107, to the nearest thousandth?

(a)  

On a standardized exam, the scores are normally distributed with a mean of 155 and a standard deviation of 25. Find the z-score of a person who scored 205 on the exam.

• 2.5

• -2

• -2.5

• 2

On a standardized exam, the scores are normally distributed with a mean of 600 and a standard deviation of 40. Find the z-score of a person who scored 520 on the exam.

• 1.5

• -2

• 2

• -1

The weight of oranges growing in an orchard is normally distributed with a mean weight of 5.5 oz. and a standard deviation of 0.5 oz. Using the empirical rule, determine what interval would represent weights of the middle 68% of all oranges from this orchard.

*Write interval in this form: a-b

(a)  

The wait times at a popular restaurant are normally distributed with a mean of 23 minutes and a standard deviation of 3.5 minutes. Using the empirical rule, what percentage of wait times will be between 16 and 30 minutes?

(a)  

Scores on the Wechsler Adult Intelligence Scale (a standard IQ test) for the 20-to-34 age group are approximately normally distributed with a mean of 100 and a standard deviation of 25.

Mensa is an elite organization that admits as members people who score in the top 2% on IQ tests. What score on the Wechsler Adult Intelligence Scale would an individual aged 20-34 have to earn to qualify for MENSA membership? (Round to the nearest hundredth.)

(a)  

Researchers in Norway analyzed data on the birth weights of 400,000 newborns over a 6-year period. The distribution of birth weight is approximately normal with a mean of 3668 grams and a standard deviation of 511 grams.

What is the first quartile of the birth weight distribution? (Round to the nearest whole number.)

(a)  

Researchers in Norway analyzed data on the birth weights of 400,000 newborns over a 6-year period. The distribution of birth weight is approximately normal with a mean of 3668 grams and a standard deviation of 511 grams.

What is the 75th percentile of the birth weight distribution? (Round to the nearest whole number.)

(a)