Mean, Median, Mode, and Range
Santa's Workshop tracks the number of toys produced each day in December. For the first 15 days, the daily toy counts were: 120, 135, 142, 118, 156, 130, 149, 138, 125, 160, 145, 152, 128, 140, 133. Calculate the mean, median, and mode of toy production for these days. Round to the nearest tenth if necessary.
Mean:138.1
Median: 138
Mode: None
The Kwanzaa Candle Company produces candles with lengths that are normally distributed. If 68% of the candles have lengths between 7.8 and 8.2 inches, what is the standard deviation of the candle lengths?
0.2
An elf can wrap an average of 50 gifts per hour with a standard deviation of 5 gifts. What is the probability that in a given hour, the elf will wrap between 45 and 55 gifts.
0.6826
Yankee candles produces candles with burn times that are normally distributed. The quality control team randomly selects 40 lamps and finds that the sample mean burn time is 35 hours with a sample standard deviation of 2.5 hours. Using the Central Limit Theorem, what is the probability that the sample mean is between 34 and 36 hours?
0.9986
Rudolph is testing new Christmas light bulbs. In a sample of 500 bulbs, he found that the mean of defective light bulbs is 20 with a standard deviation of 5. Estimate the 95% confidence interval for the mean of defective bulbs in the entire production run.
20<mean<20
The Winter Wonderland theme park tracks daily visitor numbers. For the past 10 days, the counts were: 2150, 1980, 2340, 2100, 2250, 2080, 2310, 2190, 2020, 2280. Calculate the mean, median, and mode of daily visitors.
Mean: 2,170
Median: 2,170
Mode: None
The weights of holiday turkeys are normally distributed. If 95% of turkeys weigh between 10 and 16 pounds, what is the standard deviation of turkey weights? Round to the nearest tenth.
1.5
A New Year's Eve party planner is estimating attendance. Based on previous years, attendance is normally distributed with a mean of 500 and a standard deviation of 50. If the venue capacity is 600, what is the probability that the attendance will exceed the capacity? Round to the nearest hundredth.
0.02
The Jingle Bell Factory produces sleigh bells with weights that are normally distributed with a mean of 50 grams and a standard deviation of 5 grams. If you randomly select 100 bells and calculate their average weight, what is the probability that the sample mean will be between 49 and 51 grams? Round your answer to the nearest hundredth.
0.95
The Hanukkah Dreidel Spinners Association wants to determine the average spin time of their dreidels. They randomly select 36 dreidels and find the sample mean spin time to be 12.5 seconds with a sample standard deviation of 2.2 seconds. Calculate the 90% confidence interval for the population mean spin time.
11.9<mean<13.1
During the 12 days of Christmas, a local charity received the following numbers of donations: 50, 75, 62, 88, 95, 70, 82, 78, 90, 85, 92, 83. Calculate the range and interquartile range of the donations.
Range: 45
IQR: 16.5
A holiday baking contest judges rate cookies on a scale of 1-100. The winning scores from the past 8 years were: 92, 88, 95, 90, 93, 89, 94, 91. Calculate the mean and standard deviation of the winning scores. Round your answers to the nearest tenth.
Mean: 91.5
Standard Deviation: 2.4
Snowflake sizes in a recent snowstorm are normally distributed with a mean of 0.5 cm and a standard deviation of 0.1 cm. What percentage of snowflakes are larger than 0.7 cm? Round your answer to the nearest hundredth.
2.28%
Santa's reindeer consume magic carrots to fuel their Christmas Eve flight. The number of carrots each reindeer eats is normally distributed with a mean of 30 and a standard deviation of 4. If Santa has 9 reindeer, what is the probability that their average carrot consumption on Christmas Eve will be more than 32 carrots? Round to the nearest hundredth.
The Winter Solstice Festival organizers want to estimate the average age of attendees. They randomly sample 100 people and find the sample mean age to be 34.5 years with a sample standard deviation of 8.2 years. Calculate the 95% confidence interval for the population mean age.
32.9<mean<36.1
A holiday light show runs for 20 nights. The nightly attendance data is: 520, 480, 610, 550, 590, 530, 600, 570, 540, 620, 510, 580, 560, 590, 500, 630, 570, 540, 600, 585. Calculate the range and interquartile range of the attendance.
Range:150
IQR: 55
The waiting time for a popular holiday ride at an amusement park is normally distributed with a mean of 30 minutes. If 2.5% of visitors wait more than 40 minutes, what is the standard deviation of the waiting time? Round your answer to the nearest tenth.
5
At the North Pole Christmas Eve party, elves' heights are normally distributed with a mean of 4.5 feet and a standard deviation of 0.3 feet. What percentage of elves are taller than 5 feet? Round the percentage to the hundredths place.
4.75%
The Hanukkah Dreidel Spinners Association found that spin times for their dreidels are normally distributed with a mean of 15 seconds and a standard deviation of 3 seconds. If a child spins 25 dreidels, what is the probability that the average spin time for this sample will be less than 14 seconds? Round to the nearest hundredth.
0.05
Santa's reindeer training program measures jump heights. After a new training regimen, a sample of 25 reindeer showed a mean jump height of 12.8 feet with a standard deviation of 1.5 feet. Construct a 99% confidence interval for the population mean jump height.
12.0<mean<13.6
Santa's Workshop tracks the daily production of two toy-making machines over the 12 days leading up to Christmas. The data (in toys produced per day) is as follows:
Machine A: 120, 135, 128, 142, 130, 138, 125, 140, 133, 145, 137, 132
Machine B: 115, 140, 130, 145, 125, 150, 120, 155, 135, 160, 140, 145
Calculate the mean, median, and mode for each machine's production.
The elves need to choose the most consistent machine for a special project, explain which machine you would recommend and why.
Round answers to the nearest tenth.
1.Machine A:
Mean: 133.8
Median:134
Mode: None
Machine B:
Mean:138.3
Median: 140
Mode: 140 and 145
2. The mean is the most representative value of the output data. Since Machine A's mean is higher, that would be the machine that is most consistent.
A factory produces candy canes with lengths normally distributed around a mean of 6 inches. If 16% of candy canes are longer than 6.5 inches, what is the standard deviation of candy cane lengths?
0.5
During the holiday season, a toy store's daily sales are normally distributed with a mean of $5000 and a standard deviation of $800. What is the probability of daily sales exceeding $6200? Round to the nearest thousandths.
0.067
A Christmas tree farm sells trees with heights that are normally distributed with a mean of 7 feet and a standard deviation of 1 foot. If a local community center buys 64 trees for their holiday display, what is the probability that the average height of their trees will be between 6.8 and 7.2 feet? Round to the nearest hundredth.
0.09
A survey asks 150 people to rate their favorite holiday movie on a scale of 1-10. The results have a mean of 7.5 and a standard deviation of 1.8. Construct a 95% confidence interval for the population mean rating.
7.2<mean<7.8