CH 5
0.004
According to government data, the probability that an adult was never in a museum is 15%. In a random survey of 10 adults, what is the probability that two or fever were never in a museum?
0.820
A language school tracks the number of new vocabulary words learned by students in their first month. This number is normally distributed with a mean of 95 words and a standard deviation of 15 words.
a) What percent of students learn more than 120 words? (Round to 4 decimal places)
b) The school promises students will learn at least 60 words in their first month. If they don’t, they get a partial refund. If 2,500 students enroll, how many are expected to qualify for a refund?
a)0.0478= 4.78%
b) 57 students
A researcher collects a random sample of 36 pineapples and finds their average weight is 4.8 pounds with a standard deviation of 0.9 pounds.
a) Construct a 95% confidence interval for the population mean weight. Round to one decimal place.
b) Interpret the confidence interval.
c) What is the margin of error?
a) (4.5, 5.1)
b) We are 95% confident the true mean weight of pineapples is between 4.5 and 5.1 pounds.
c) 0.3 pounds
According to a recent poll, 65% of adults believe climate change is a major threat. A researcher suspects that fewer people in a rural area believe this. She surveys 400 residents, and 240 say they believe it is a major threat.Is there sufficient evidence to support your suspicion at the 𝛼 = 0.01 level of significance?
a) State the null and alternative hypotheses
b) What is the P-value? (Round to three decimal places)
c) Do you reject H0? Why or why not?
d) State the conclusion
a) H0: p=0.65
H1: p< 0.65
b) 0.018
c)Do not reject
d) There is not enough evidence to suport the claim that fewer rural residents belive climate change is major threat compared to the naitonal figure.
About 40% of U.S. consumers say they prefer online shopping over in-store shopping.
If five consumers are selected at random, what is the probability that all five prefer online shopping?
P=0.40,
According to a survey, 65% of employees admit to taking office supplies for personal use. A random sample of 25 employees is selected.Find each probability below using your TI-84 calculator. Round each answer to 4 decimal places.Write out the calculator function you used, and circle your final answer.
a) Find the probability that exactly 18 of the 25 employees take office supplies.
b) Find the probability that fewer than 20 employees take office supplies.
a) 0.1389- binompdf(25, 0.65, 18)
b) 0.9132- binomcdf(25, 0.65, 19)
A vitamin supplement company tracks the improvement in energy levels (measured in points) after 30 days of use. The improvement is normally distributed with a mean of 12.5 points and a standard deviation of 3.2 points.
a) What percent of users improve by more than 18 points? (Round to 4 decimal places)
b) The company guarantees an improvement of at least 7 points. If a user improves less than 7 points, they get a refund. Out of 10,000 users, how many will get a refund? (Round to nearest whole number)
a) 0.0800
b) 787 users
From a random sample of 40 watermelons, the mean weight is found to be 22 pounds with a standard deviation of 5.1 pounds.
a) Find a 95% confidence interval for the mean weight of watermelons. Round to one decimal place.
b) Interpret your confidence interval.
c) What is the margin of error for this survey?
a) (20.4,23.6)
b) We are 95% confident that the true mena weight of all the watermelons is between 20.4 and 23.6 pounds
c) 1.6 lbs
A national survey reports that 48% of Americans own a pet dog. A local community group believes that the proportion of dog owners in their town is higher than the national figure. They survey 500 randomly selected residents, and 260 of them own a dog.Is there sufficient evidence to support your suspicion at the 𝛼 = 0.05 level of significance?
a) State the null and alternative hypotheses
b) What is the P-value? (Round to three decimal places)
c) Do you reject H0? Why or why not?
d) State the conclusion
a) H0: p=0.48
H1: p>0,48
b) 0.037
c) Reject H0
d) There is sufficient evidence to support that the proportion of the do owners in the town is greater than the national porportion of 48%
Approximately 65% of U.S. households own a pet.
If three households are selected at random, what is the probability that none of them own a pet?
0.043
c) Find the probability that at least 20 employees take office supplies.
d) Find the expected number of employees that take office supplies.
c) 0.0868
d) 16.25
The scores on a final exam for a college statistics course are normally distributed with a mean of 78 and a standard deviation of 6.5.
Answer each question using the information above.
Write out the function or steps you did on the TI-84, and then circle your final answer.
a) What percent of students scored more than 90? Round to 4 decimal places.
b) A passing grade is 60. If there are 120 students, how many are expected to fail the exam? Round to the nearest whole number.
c) The professor wants to give a special certificate to the top 15% of the class. What is the minimum score a student must earn to receive this certificate? Round to the nearest whole number.
a) 3.26%
b)0
c) 86
A coffee shop finds the average caffeine content in a cup of coffee is 95 mg with a standard deviation of 14 mg. A random sample of 49 cups is selected.
a) What are the values of μₓ̄ and σₓ̄?
b) What is the probability that the sample mean is greater than 100 mg?
c) Would a sample mean below 90 mg be unusual?
a) μₓ̄ = 95, σₓ̄ = 2.0
b) P(𝑥̄ > 100) ≈ 0.0062
c) P(𝑥̄ < 90) ≈ 0.0062 → Yes, it’s unusual
According to a Pew Research Center poll, 55% of U.S. adults support the legalization of recreational marijuana use. You suspect that a higher proportion of California residents support legalization. In a survey of 600 randomly selected Californians, 360 of them support recreational marijuana legalization.Is there sufficient evidence to support your suspicion at the 𝛼 = 0.01 level of significance?
a) State the null and alternative hypotheses
b) What is the P-value? (Round to three decimal places)
c) Do you reject H0? Why or why not?
d) State the conclusion
a) H0: p=0.55 proportion in California equals the national proportion)
H1: p>0.55p (proportion in California is greater than the national proportion)
b) 0.007
c) Reject
d) There is sufficient evidence to support that a higher proportion of californians support legalization compared to the national proportion of 55%
A conference is organizing a lunch menu. There are 12 dessert options, and the organizers will choose 4 different desserts to offer attendees.
495 ways
According to CITA, 72% of adult Americans would rather give up chocolate than their cell phone. In a simple random sample of 300 households, determine the mean and standard deviation number who would rather give up chocolate rather than their cell phone.
216
Suppose that EverGo Battery Co. produces a rechargeable battery whose life is normally distributed with a mean of 500 hours and a standard deviation of 60 hours.Answer each question using the information above.Write out the function or steps you did on the TI-84, and then circle your final answer.
a) What proportion of EverGo batteries last more than 580 hours? (Round to 4 decimal places.)
b) A battery is considered defective if it lasts less than 410 hours.If EverGo manufactures 25,000 batteries, how many would you expect to be defective?Round to the nearest whole number.
c) A battery is covered under warranty if it lasts fewer hours than a certain threshold. EverGo wants to limit warranty claims to 1% of its batteries.What should they advertise as the warranty life?Round to the nearest 10 hours.
a) 0.0912
b) 1,670 defective batteries
c) 380 hours
The scores on a standardized English proficiency test have a mean of 75 and a standard deviation of 12. Suppose a random sample of 81 test scores is taken.
a) Describe the sampling distribution of the sample mean (xˉ) (give the values of μxˉ and σxˉ).
b) What is the probability that the sample mean score is less than 72? Round to 4 decimal places.
c) Would it be unusual for a sample mean score to be greater than 78? Why or why not?
a) sample mean: 75; standard dev. smaple mean= 1.333
b) 0.0122
c) yes, it would be unusual
A poll was conducted to determine the proportion of college students who own a laptop. Of the 180 college students surveyed, 68% of them owned a laptop.
a) Construct and interpret a 99% confidence interval for the proportion of college students who own a laptop. Round to three decimal places.
b) If the researchers want the margin of error to be no more than 3% (0.03), what sample size is required, using a prior estimate of 68%?
a) (0.588, 0.768)
b) 1,605
336 ways
The number of people with blood type O-neg based on a simple random sample of size 10 is recorded. According to the American red cross, 7% of the people in the united States have blood type O-negative. Find the probabilities:
a) Exactly 8 people with blood type O-negative.
b) At most 3 people with blood type O-negative.
c) More than 7 people with a blood type of O-negative.
d)Less than 6 people with blood type O-negative.
e)From 4 to 6, inclusively , with blood type O-negative
a) 2.244e-8
b)0.996
c) 2.282e-8
d) 0.99998
e)0.0036
The weight of packages delivered by a shipping company is normally distributed with a mean of 12.3 pounds and a standard deviation of 2.1 pounds.
Answer each question using the information above.
Write out the function or steps you did on the TI-84, and then circle your final answer.
a) What percent of the packages weigh less than 10 pounds? Round to 4 decimal places.
b) Packages weighing more than 15 pounds require a special handling fee. If the company ships 2,000 packages, how many will require the fee? Round to the nearest whole number.
c) The company wants to label the lightest 5% of packages as “fragile.” What is the maximum weight a package can be and still be considered in the bottom 5%? Round to the nearest tenth of a pound.
a) 13.67 %
b) 199 packages
c)8.9 pounds
A statistics exam has a mean score of 82 and a standard deviation of 10. A random sample of 64 students is taken.
a) What are the values of μₓ̄ and σₓ̄?
b) What is the probability the sample mean is less than 80?
c) Would a sample mean greater than 85 be unusual?
a) μₓ̄ = 82, σₓ̄ = 1.25
b) P(𝑥̄ < 80) ≈ 0.1056
c) P(𝑥̄ > 85) ≈ 0.0082 → Yes, it’s unusual
A simple random sample of 150 adult Americans is taken, and it is found that 36 of them have associate degrees.
a) Find a point estimate for the proportion of adult Americans that have associate degrees.
b)Construct a 90% confidence interval for the proportion of adult Americans that have associate degrees. Round to one decimal place.
c) Interpret your confidence interval
d) Is it possible that the true proportion is less than 20%? Why or why not?
e) Is it likely that the true proportion is less than 20%? Why or why not?
a) 0.24
b) (0.183, 0.297)
c) We are 90% confident that the true porportion of adult americans with associate degres is between 18.3% and 29.7%
d) Yes 20% lies within the confidence interval
e) No, becuase the point estimate is 24% and the confidence interval is mostly above 20%