6. If the probability of a defective bolt is 0.1, find (a) the mean (b) the standard deviation for the distribution of defective bolts in a total of 400.
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- The amounts of electricity bills for all households in a particular city have an approximately normal distribution with a mean of $135 and a standard deviation of $25. Let I be the mean amount of electricity bills for a random sample of 24 households selected from this city. Find the mean and standard deviation of4. The delivery time for all food orders at a fast food restaurant have a mean of 6.7 minutes and a standard deviation of 2.1 minutes. a. Assume a normal distribution and compute the probability that an order is delivered in less than 6 minutes. prob = b. Find the probability that the mean of 40 orders is less than 6 minutes. prob = c. Find the probability that serving 40 orders takes less than a total of 4.5 hours. prob = %3DAssume that adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation of 15. Find the probability of randomly selected adult has an IQ score less than 115.
- The lengths of pregnancies are normally distributed with a mean of 267 days and a standard deviation of 15 days. a. Find the probability of a pregnancy lasting 309 days longer. b. If the length of pregnancy is in the lowest 2%then the baby is premature. Find the length that separates premature babies from those who are not PrematureThe blood sugar levels of a person follows a normal curve with an average of 4.7mmol/L and a standard deviation of 1.4. In 2014, it is estimated that 8.5% of people around the world have diabetes. 1. Indicate whether the distribution to be used in answering the problem is a normal distribution 2. If yes, solve for the probability a. The probability of getting a random person with a high blood sugar level greater than 7mmol/L. b. The probability of getting a random sample of 150 people with less than 10% having diabetes c. The probability of getting a random sample of 60 people with less than 9% having diabetes d. The probability of getting a random sample of 150 people with a mean blood sugar level less than 5mmol/L. e. The probability of getting a random sample of 25 people with a mean of blood sugar level greater than 4.5mmol/L.Sketch the distribution, show the mean and standard error, and shade the part of the curve corresponding to your calculation. Suppose that at a large university, 34% of the students decide to take their classes online. 2. Now, if the researcher takes a different sample of 1000 students, what is the probability that at least 35% of the new sample will decide to take classes online?
- The probability that a randomly chosen student in a statistics class submits his/her homework on time is 0.12. There is 35 student in the class. Each student does his/her homework independently. What is the standard deviation of X, where X is the number of students who submit the homework on time?The daily electric consumption of two houses were recorded. House A has consumes 375W (mean) the standard deviation is 15W. While House B uses 250W (mean), the standard deviation is 22W. 1. Find the probability for each house that the electric usage will not exceed 400W.2. Find the probability that both houses will exceed 400W in usage.3.Given the probability of 0.02, how much electricity must House B consume to avoid exceeding?Suppose that the average number of hurricanes is 32 per year with a standard deviation of 2.8 and follow a normal distribution. What is the probability that we will have more than 31 hurricanes this year in a decimal form?
- The percent of fat calories that a person consumes each day is normally distributed with a mean of about 35 and a standard deviation of about ten. Suppose that 9 individuals are randomly chosen. Let X = average percent of fat calories. For the group of 9, find the probability that the average percent of fat calories consumed is more than six. (Round your answer to four decimal places.)Suppose that the distribution of the grades of students in MAPEH performance 1 is roughly normally distributed with a mean of 85 and a standard deviation of 5 a. Between what values do we expect the grades of the middle 68% of the MAPEH students in performance 1 lie? b. Suppose you randomly select 16 MAPEH students, find the probability that the average grades of these students is at least 86. c. A MAPEH student whose grades lies in the upper 1% of the distribution (inclusive of the 1% cutoff) is considered extremely performing in Performance 1. Can you say that Jazzer, a randomly selected student who obtained a grade of 95, is one of those who performed extremely in Performance 1?Assume time to failure density function (in months) of transplanted kidneys has a Weibull distribution with shape factor of 3 and scale of 6. Use R and answer the following questions (enter your answers with 3 decimal points):