Assume that the readings on the thermometers are normally distributed with a mean of 0 and a standard deviation of 1C..
1. Assume that the readings on the thermometers are normally distributed with a mean of 0◦ and a standard deviation of 1◦C. A thermometer is randomly selected and tested. Find the probability of each reading in degrees.
a. Between 0 and 0.65:
b. Between −0.6 and 0:
c. Between −1.01 and 0.56:
d. Less than 2.05:
e. Greater than −0.64:
2. Using diaries for many weeks, a study on the lifestyles of visually impaired students was conducted. The students kept track of many lifestyle variables including how many hours of sleep were obtained on a typical day. Researchers found that visually impaired students averaged 9.87 hours of sleep, with a standard deviation of 1.1 hours. Assume that the number of hours of sleep for these visually impaired students is normally distributed.
a. What is the probability that a visually impaired student gets less than 6.1 hours of sleep?
b. What is the probability that a visually impaired student gets between 6.5 and 7.89 hours of sleep?
3. The extract of a plant native to Taiwan has been tested as a possible treatment for Leukemia. One of the chemical compounds produced from the plant was analyzed for a particular collagen. The collagen amount was found to be normally distributed with a mean of 61 and standard deviation of 9.8 grams per mililiter.
a. What is the probability that the amount of collagen is greater than 60 grams per mililiter?
b. What is the probability that the amount of collagen is less than 90 grams per mililiter?
c. What percentage of compounds formed from the extract of this plant fall within 1 standard deviation of the mean?
4. Determine the following z-scores:
a. z0.1 =
b. z0.025 =
5. Find the z-score such that:
a. The area under the standard normal curve to its left is 0.5 z = ____
b. The area under the standard normal curve to its left is 0.9826 z = ____
c. The area under the standard normal curve to its right is 0.1423 z = ____
d. The area under the standard normal curve to its right is 0.9394 z = ____
6. The lifetime of lightbulbs that are advertised to last for 4100 hours are normally distributed with a mean of 4400 hours and a standard deviation of 300 hours. What is the probability that a bulb lasts longer than the advertised figure?
7. A new car that is a gas- and electric-powered hybrid has recently hit the market. The distance travelled on 1 gallon of fuel is normally distributed with a mean of 65 miles and a standard deviation of 7 miles. Find the probability of the following events:
a. The car travels more than 69 miles per gallon. Probability = ________
b. The car travels less than 58 miles per gallon. Probability = ________
c. The car travels between 61 and 71 miles per gallon. Probability =________
8. Select True or False
1. A random variable X is normally distributed with a mean of 150 and a variance of
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