(1) Consider a normal distribution with mean 38 and standard deviation 3. What is the probability a value selected at random from this distribution is greater than 38? (Round your answer to two decimal places.)

(4) Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.) μ = 14.1; σ = 4.4 P(10 ≤ x ≤ 26)=

(5) Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.)

μ = 15.0; σ = 2.8 P(8 ≤ x ≤ 12) =

(6) Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.) μ = 107; σ = 11 P(x ≥ 120) =

(7) Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.)

μ = 2.1; σ = 0.39 P(x ≥ 2) =

(8) Find z such that 4.2% of the standard normal curve lies to the left of z. (Round your answer to two decimal places.)
z =

Sketch the area described.

(9)Find z such that 2.7% of the standard normal curve lies to the right of z. (Round your answer to two decimal places).

z=

Sketch the area described

(10) Find the z value such that 86% of the standard normal curve lies between −z and z. (Round your answer to two decimal places.)
z =

Sketch the area described.

(11) Thickness measurements of ancient prehistoric Native American pot shards discovered in a Hopi village are approximately normally distributed, with a mean of 5.3millimeters (mm) and a standard deviation of 0.8 mm. For a randomly found shard, find the following probabilities. (Round your answers to four decimal places.)

(a) the thickness is less than 3.0 mm


(b) the thickness is more than 7.0 mm


(c) the thickness is between 3.0 mm and 7.0 mm

(12) Quick Start Company makes 12-volt car batteries. After many years of product testing, the company knows that the average life of a Quick Start battery is normally distributed, with a mean of 45.2 months and a standard deviation of 8.1 months.

(a) If Quick Start guarantees a full refund on any battery that fails within the 36-month period after purchase, what percentage of its batteries will the company expect to replace? (Round your answer to two decimal places.)
%

(b) If Quick Start does not want to make refunds for more than 11% of its batteries under the full-refund guarantee policy, for how long should the company guarantee the batteries (to the nearest month)?
months

(13) How much should a healthy kitten weigh? Suppose that a healthy 10-week-old (domestic) kitten should weigh an average of μ = 25.3 ounces with a (95% of data) range from 15.0 to 35.6 ounces. Let x be a random variable that represents the weight (in ounces) of a healthy 10-week-old kitten. Assume that x has a distribution that is approximately normal.

(a) The empirical rule (Section 7.1) indicates that for a symmetrical and bell-shaped distribution, approximately 95% of the data lies within two standard deviations of the mean. Therefore, a 95% range of data values extending from μ − 2σ to μ + 2σ is often used for "commonly occurring" data values. Note that the interval from μ − 2σ to μ + 2σ is 4σ in length. This leads to a "rule of thumb" for estimating the standard deviation from a 95% range of data values.Estimating the standard deviation

For a symmetric, bell-shaped distribution,≈

=

where it is estimated that about 95% of the commonly occurring data values fall into this range.Estimate the standard deviation of the x distribution. (Round your answer to two decimal places.)
oz

(b) What is the probability that a healthy 10-week-old kitten will weigh less than 14 ounces? (Round your answer to four decimal places.)


(c) What is the probability that a healthy 10-week-old kitten will weigh more than 33 ounces? (Round your answer to four decimal places.)


(d) What is the probability that a healthy 10-week-old kitten will weigh between 14 and 33 ounces? (Round your answer to four decimal places.)


(e) A kitten whose weight is in the bottom 7% of the probability distribution of weights is called undernourished. What is the cutoff point for the weight of an undernourished kitten? (Round your answer to two decimal places.)
oz

(14) A relay microchip in a telecommunications satellite has a life expectancy that follows a normal distribution with a mean of 93 months and a standard deviation of 3.1 months. When this computer-relay microchip malfunctions, the entire satellite is useless. A large London insurance company is going to insure the satellite for 50 million dollars. Assume that the only part of the satellite in question is the microchip. All other components will work indefinitely.

(a) For how many months should the satellite be insured to be 90% confident that it will last beyond the insurance date? (Round your answer to the nearest month.)
months

(b) If the satellite is insured for 84 months, what is the probability that it will malfunction before the insurance coverage ends? (Round your answer to four decimal places.)


(c) If the satellite is insured for 84 months, what is the expected loss to the insurance company? (Round your answer to the nearest dollar.)
$  

(d) If the insurance company charges $3 million for 84 months of insurance, how much profit does the company expect to make? (Round your answer to the nearest dollar.)

(14) The amount of money spent weekly on cleaning, maintenance, and repairs at a large restaurant was observed over a long period of time to be approximately normally distributed, with mean μ = $627 and standard deviation σ = $46.

(a) If $646 is budgeted for next week, what is the probability that the actual costs will exceed the budgeted amount? (Round your answer to four decimal places.)


(b) How much should be budgeted for weekly repairs, cleaning, and maintenance so that the probability that the budgeted amount will be exceeded in a given week is only 0.14? (Round your answer to the nearest dollar.)

Suppose three competing airlines each schedule their own flight to Waco which arrives there between 2:00 and 3:00 pm according to a continuous uniform distribution. All three flights are mutually independent.

(a) If Ralph shows up at the airport at 2:00 and decides he will watch all three arrivals, what is the expected time that he observes the third and last arrival?

(b) If each airline’s flight only stays on the ground for 10 minutes, find or estimate the probability that all 3 airlines will have a plane on the ground at Waco at some point in the hour from 2:00 to 3:00.

The weight of Coca Cola cans is being analyzed. Thirteen cans, randomly selected from the process, are measured, and the results are as follows (in fluid ounces): 16.01, 16.01, 16.02, 16.03, 16.05, 16.07, 16.02, 16.01, 16.00, 16.01, 16.07, 16.05 and 16.05. Determine the following using the formulas (include all the formulas) and confirm your answer using Minitab. a. Average b. Sample standard deviation c. Median d. Mode e. Range f. Construct histogram using Minitab and determine Kurtosis and skewness (use Minitab only), comment on these values in relation to the histogram.

URGENT

a) samples of rejuvenated mitochondria are mutated (defective) with probability 0.2.find the probability you need to examine at least 6 samples to find 2 samples containing mutations.report answers to 3 decimal places.(try to type your answer)

b) what is the first,second,third quartile, and the outlier of 15,29,30,34,35,36,37,37,37,40,42,42,44,44,45,46,49,51,53,54?(try to type your answer)

c) the claim is that the IQ scores of statistics professors are normally distributed, with a mean less than 126. A sample of 17 professors had a mean IQ score of 125 with a standard deviation of 10. find the value of the test statistic?

Construct a histogram of your empirical data using eight bars and then five bars. For consistency's sake, for eight bars use the class width of 0.125. So, your first bar will be 0.000-0.124, your next bar will be 0.125 - 0.249, etc. For five bars, use the class width of 0.2. So, your first bar will be 0.00-0.19, your next bar will be 0.2-0.39, etc. Upload both pictures of your histograms. ***Below are my 50 random numbers. What do I need to show? I am confused on what exactly I need to show. Can you help me on these?

0.9          1.0          0.7          0.0          0.8         

0.0          0.8          0.2          0.0          1.0

0.5          0.2          0.5          0.4          0.0

0.8          0.1          0.4          0.2          1.0

0.1          0.1          0.9          0.7          0.1

0.9          1.0          0.9          0.2          0.4

0.0          1.0          0.5          0.9          0.4

0.9          0.0          0.0          1.0          0.3

0.4          0.8          0.9          0.6          0.5

0.4          0.5          0.3          0.7          1.0

A rural county hospital offers several health services. The hospital administrators conducted a poll to determine whether the residents’ satisfaction with the available services depends on their gender. A random sample of 1000 adult county residents was selected. The gender of each respondent was recorded and each was asked whether he or she was satisfied with the services offered by the hospital. The resulting data are shown in the table below. Using a significance level of 0.05, conduct an appropriate test to determine if, for adult residents of this county, there is an association between gender and whether or not they were satisfied with services offered by the hospital.

Adam tabulated the values for the average speeds on each day of his road trip as 60.5, 63.2, 54.7, 51.6, 72.3, 70.7, 67.2, and 65.4 mph he wishes to construct a 98% confidence interval what value of t* should Adam use to construct the confidence interval?

Dr. Patel is concerned about the long wait times in his office. The following table presents six random observations for the patient waiting times over a period of 10 days.

1. Dr. Patel is willing to use three-sigma limits. Use the given data and the factors from Table 3.1 (page 110) to construct R-chart and -chart.
2. Is the process in statistical control? Explain.
3. If patient surveys indicate that they are willing to wait between 10 and 30 minutes before seeing Dr. Patel, is the process capable of meeting this demand at the three-sigma level?

Table 3.1

Factors For Calculating Three Sigma Limits for the x¯x¯ -Chart and R-Chart

A random sample of 15 chemists from Washington state shows an average salary of $46613 with a standard deviation of $775. A random sample of 24 chemists from Florida state shows an average salary of $47757 with a standard deviation of $872. A chemist that has worked in both states believes that chemists in Washington make a different amount than chemists in Florida. At α α =0.01 is this chemist correct? Let Washington be sample 1 and Florida be sample 2. The correct hypotheses are: H 0 : μ 1 ≤ μ 2 H 0 : μ 1 ≤ μ 2 H A : μ 1 > μ 2 H A : μ 1 > μ 2 (claim) H 0 : μ 1 ≥ μ 2 H 0 : μ 1 ≥ μ 2 H A : μ 1 < μ 2 H A : μ 1 < μ 2 (claim) H 0 : μ 1 = μ 2 H 0 : μ 1 = μ 2 H A : μ 1 ≠ μ 2 H A : μ 1 ≠ μ 2 (claim) Correct

Since the level of significance is 0.01 the critical value is 2.736 and -2.736

The test statistic is: Incorrect(round to 3 places)

The p-value is: Incorrect(round to 3 places)

A custodian wishes to compare two competing floor waxes to decide which one is best. He believes that the mean of WaxWin is less than the mean of WaxCo.

In a random sample of 12 floors of WaxWin and 16 of WaxCo. WaxWin had a mean lifetime of 25.5 with a standard deviation of 6.7 and WaxCo had a mean lifetime of 30.4 with a standard deviation of 10.6. Perform a hypothesis test using a significance level of 0.05 to help him decide.

Let WaxWin be sample 1 and WaxCo be sample 2

The correct hypotheses are:

• H0:μ1≤μ2H0:μ1≤μ2
  HA:μ1>μ2HA:μ1>μ2(claim)
• H0:μ1≥μ2H0:μ1≥μ2
  HA:μ1<μ2HA:μ1<μ2(claim)
• H0:μ1=μ2H0:μ1=μ2
  HA:μ1≠μ2HA:μ1≠μ2(claim)

Since the level of significance is 0.05 the critical value is -1.707
The test statistic is: (round to 3 places)
The p-value is: (round to 3 places)

A researcher is interested in seeing if the average income of rural families is greater than that of urban families. To see if his claim is correct he randomly selects 20 families from a rural area and finds that they have an average income of $66691 with a standard deviation of $794. He then selects 12 families from a urban area and finds that they have an average income of $69126 with a standard deviation of $978. Perform a hypothesis test using a significance level of 0.01 to help him decide.

Let the rural families be sample 1 and the urban families be sample 2.

The correct hypotheses are:

• H0:μ1≤μ2H0:μ1≤μ2
  HA:μ1>μ2HA:μ1>μ2(claim)
• H0:μ1≥μ2H0:μ1≥μ2
  HA:μ1<μ2HA:μ1<μ2(claim)
• H0:μ1=μ2H0:μ1=μ2
  HA:μ1≠μ2HA:μ1≠μ2(claim)

Since the level of significance is 0.01 the critical value is 2.532
The test statistic is: (round to 3 places)
The p-value is: (round to 3 places)

You may need to use the appropriate appendix table or technology to answer this question.

A simple random sample of 60 items resulted in a sample mean of 90. The population standard deviation is

σ = 15.

(a)

Compute the 95% confidence interval for the population mean. (Round your answers to two decimal places.)

( )to( )

(b)

Assume that the same sample mean was obtained from a sample of 120 items. Provide a 95% confidence interval for the population mean. (Round your answers to two decimal places.)

( )to( )

(c)

What is the effect of a larger sample size on the interval estimate?

A. A larger sample size does not change the margin of error.

B. A larger sample size provides a smaller margin of error.    

C. A larger sample size provides a larger margin of error.

Suppose that there are 100 students entering the Master’s of Business Administration program. Of these students, 20 have two years of work experience, 30 have three years of work experience, 15 have four years of work experience, and 35 have five or more years of work experience.

a) One of the students is selected at random. What is the probability that this student has at least three years of work experience?

b) The selected student has at least three years of work experience. What is the probability the student has four years of work experience?

c) Three students are selected at random. Calculate the probability that all three students have five or more years of work experience. Describe the key assumption required to make the calculation and comment on whether the assumption is reasonable.

d) Would it be reasonable to use the probability calculated in part a) as an estimate of the proportion of students entering the MBA degree program who have at least three years of work experience? Explain your answer. Limit your explanation to at most five sentences.

Consider a sample of size 100 drawn from a population that obeys an unknown distribution. It is known that the population-variance (of some quality characteristic) is 6. Let µ denote the population-mean. Consider the following test of a hypothesis about µ.

H₀ : µ = 70

H₁ : µ ≠ 70

(a) Calculate Z_0.005. Explain the meaning of Z_0.005. (b) If the sample mean is observed to be 71, would you reject H₀ with 99% confidence? What is the p-value of the sample mean? (c) If the sample mean is observed to be 71, and the sample size is 30 (instead of 100), would you reject H₀ with 99% confidence?

HIV-related deaths and mid-year population by age group in Country Y in 2003 are given below

(d) Calculate the age-specific HIV-related death rates for country Y in 2003, and complete the above table. (4pts)

(e) Can you conclude that a person living in country X has a risk of dying from HIV that is 1.2 times as high as a person living in country Y? Give a reason for your answer (2pts)

Our event of interest is whether a defective chip is found in a set of chips, and let Y be the number of chips that must be sampled until a defective one is found. The researchers estimate the probability of a defective chip at 30%. What is the probability that the 8th selected chip be the first defective one?

Consider the following time series data: