The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 48 ounces and a standard deviation of 3 ounces.Use the Standard Deviation Rule, also known as the Empirical Rule (see image below).  Do not use normalcdf on your calculator.Suggestion: sketch the distribution in order to answer these questions.a) 99.7% of the widget weights lie between  and b) What percentage of the widget weights lie between 45 and 57 ounces?  %c) What percentage of the widget weights lie below 54 ?

Question

The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 48 ounces and a standard deviation of 3 ounces.

Use the Standard Deviation Rule, also known as the Empirical Rule (see image below).  Do not use normalcdf on your calculator.

Suggestion: sketch the distribution in order to answer these questions.

a) 99.7% of the widget weights lie between  and 

b) What percentage of the widget weights lie between 45 and 57 ounces?  %

c) What percentage of the widget weights lie below 54 ? 

Expert Answer

Want to see the step-by-step answer?

Check out a sample Q&A here.

Want to see this answer and more?

Experts are waiting 24/7 to provide step-by-step solutions in as fast as 30 minutes!*

*Response times may vary by subject and question complexity. Median response time is 34 minutes for paid subscribers and may be longer for promotional offers.
Tagged in
Math
Statistics

Advanced Topics in Statistics

Related Statistics Q&A

Find answers to questions asked by students like you.

Q: How to provide statistical interpretation of the coefficient, standard error, t-stat and p value of ...

A: Regression Coefficient:The regression coefficient ​corresponding to a given explanatory variable can...

Q: Help

A: Test statistic:The test statistic for hypothesis test for proportion is given by: 

Q: Births are approximately uniformly distributed between the 52 weeks of the year. 1 1 sxs53 f(x) = 52

A: Solution:Continuous uniform distribution:A random variable X is said to have the rectangular distrib...

Q: 63% of all students at a college still need to take another math class. If 4 students are randomly s...

A: Hey there! Thank you for posting the question. Since your question has more than 3 parts, we are sol...

Q: Consider a binominal experiment with 2 trials and p=0.4 a. Compute the probability of 1 success f(1)...

A: Given binomial experiment with n = 2 and p = 0.4The binomial probability for x number of success is ...

Q: Explain the four different types of sampling and give an example of each.

A: Different types of sampling methods with examples.Types of random samplings(1) Simple random samplin...

Q: Jobs and productivity! How do banks rate? One way to answer this question is to examine annual profi...

A: Calculation of confidence interval:The mean is calculated using the Excel software. After entering t...

Q: About 8% of the population has a particular genetic mutation. 1000 people are randomly selected.Find...

A: From the given information, about 8% of the population has a particular genetic mutation and there a...

Q: ive attached it below

A: The number of chocolate chips in a bag of chocolate chip cookies is normally distributed with mean 1...

Q: When do you use the t-statistic and what is the advantage over the z-statistic?

A: Conditions for using t statistic: The t statistic is used in the hypothesis testing, for testing the...

Q: r9o1010 Au cimal places) sadle Cx03.9 63 The average score of local students on a college entrance e...

A: From the provided information, the average (μ) and standard deviation (σ) of local students on a col...

Q: Today, the waves are crashing onto the beach every 5.3 seconds. The times from when a person arrives...

A: Let X be random variable uniformly distributed between 0 and 5.3 seconds.Denote X as the time from a...

Q: 5. Suppose that the probability of obtaining zero defective items in a sample of 50 items off the as...

A: It is given that P(getting zero defective items) is 0.34 and P(getting 1 defective items) is 0.46.

Q: I cant find an example for how to solve this. Help would be so great! Thank you

A: Margin of error:The formula of margin of error for confidence interval is as follows:

Q: In Hawaii, the rate of motor vehicle theft is 384 thefts per 100,000 vehicles. A large parking struc...

A: Computation of mean, λ:The mean value is calculated as follows:

Q: According to securelist, 71.8% of all email sent is spam. A system manager at a large corporation be...

A: a)The hypotheses for the test is given below.

Q: Describe the distribution of this variable by commenting on the shape (modality (how many peaks), sy...

A: Form the given graphs1st graph is uniformly distributed2nd graph is skew distributed (right skewed d...

Q: a previous analysis of paper boxes showed that the standard deviation of their lengths is 13 millime...

A: It is given that confidence level is 0.95, standard deviation is 13 and margin of error E is 4.Here,

Q: Statistics Question

A: a. State the null and alternative Hypotheses: Null Hypothesis: H0: There is no difference in means o...

Q: Find k such that P(-k < Z < k) = .6970  it might help to sketch the situation

A: To value of k can be determine as:By using Z-table,

Q: How many ways are there to choose first, second, and third prizes in an art contest with 18 entries?

A: Introduction:According to the permutation rule, if r distinct items are to be chosen from n items wi...

Q: I have to draw a P-Value graph using variables I calculated in a Chi-square test using Phstat in Mic...

A: Given Chi square test,Critical value = 12.59test statistic = 5.61p value = 0.47In chi square test th...

Q: Assume the random variable X has a binomial distribution with the given probability of obtaining a s...

A: Given datan = 18p= 0.8Applying Binomial theoremProbability of x success out of n trial is given by

Q: Comparison between two diets in obese children, one low-fat and one low-carb 8 week intervention wit...

A: A).The standard deviations of low-fat and low-carb groups are 8.4 and 7.7 respectively. The sample s...

Q: 6. Suppose a researcher used data on a group of third year students at MIT to estimate the following...

A: According to the provided information, the fitted regression line is

Q: 4. Suppose a new sample is chosen and you got the following estimated OLS line: predicted birthweigh...

A: Introduction:Effect of scale change of the predictor, on the regression coefficients:Suppose x denot...

Q: Find the standard deviation of the distribution in the following situations. (a) MENSA is an organiz...

A: a)It is given that the mean is 100.The IQs in the top 2% of the population represents the area of 0....

Q: calculate the probability of exactly 3 successes in 4 tries. p= 0.2

A: Given:n = 4, r= 3, p = 0.2Consider that the random variable X follows a binomial distribution with p...

Q: Facebook provides a variety of statistics on its Web site that detail the growth and popularity of t...

A: It is given that mean and standard deviation are 28 and 5, respectively.

Q: 4. A researcher wanted to examine the effect of a new math study skills program on second graders. F...

A: Hey there! Thank you for posting the question. Since your question has more than 3 parts, we are sol...

Q: Assume that a procedure yields a binomial distribution with a trial repeated n=13n=13 times. Use eit...

A: Giventotal number of trails = n = 13probability of success = p = 0.46To find the probability of 1 su...

Q: A manufacturer knows that their items have a normally distributed lifespan, with a mean of 14.4 year...

A: Given information:Mean, µ=14.4Standard deviation, σ=3.8Sample size, n=23

Q: The correlation coefficient for this relationship between the X variable and the Y variable would pr...

A: Correlation coefficient:It measures the relationship between two variables. The range of correlation...

Q: what would the 95% confidence limits for a sample of 120 with a mean of 51 and a standard deviation ...

A: It is given that mean and standard deviation are 51 and 12, respectively.

Q: Based on a​ survey, assume that 27​% of consumers are comfortable having drones deliver their purcha...

A: A binomial experiment is a discrete probability experiment which is repeated for a fixed number of t...

Q: Please show TI 84 steps

A: Consider X to be the random variable, defined as the lead level in water specimens with sample mean ...

Q: Find the​ z-scores that separate the middle 48​%of the distribution from the area in the tails of th...

A: Computation of probability of the area above and below the 48% of the distribution from the area:Fro...

Q: Appliance ownership- the probability that a person owns a microwave oven is 0.75, that a person owns...

A: the probability that a person owns a micro oven P(Oven) = 0.75probability that person owns a compact...

Q: 29. Surgical complications : A medical researcher wants to construct a 99% confidence interval for t...

A: It is given that margin of error (E) is 0.04 and the confidence level is 99%.

Q: suppose an individual was studying temperature's effect on crime rate. The researcher looked at 6 ra...

A: Solution:The sample mean is obtained below:From the given information, number of observations is 6 a...

Q: a normal population has a mean of 28 and a standard deviation of 5. what proportion of the populatio...

A: It is given that mean and standard deviation are 28 and 5, respectively.

Q: NeverReady batteries has engineered a newer, longer lasting AAA battery. The company claims this bat...

A: The probability of the sample mean lifetime is 16.7 hours or less is 0.0202 and it is obtained below...

Q: A normal population has a mean of 56 and a standard deviation of 11. You select a random sample of 9...

A: (a)The probability that the sample mean is greater than 58 is,

Q: To estimate the mean score ? of those who took the Medical College Admission Test on your campus, yo...

A: Part-aGivenStandard deviation = 6.5According to 68-95-99.7 rule with in one standard deviation of me...

Q: Jay can remember only the area code and the first 3 digits of his friend’s phone number.  He also kn...

A: The total number of 4 digits and last digit is not a zero is,1st digit is 0 to 92st digit is 0 to 93...

Q: #4: Suppose that X1,... , X7n is an i.i.d. random sample drawn from a U[a, 1] uniform distribution, ...

A: Click to see the answer

Q: Find a value of the standard normal random variable z ​, call it z 0z0​, such that the following pro...

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If y...

Q: The population mean annual salary for environmental compliance specialists is about ​$63 comma 00063...

A: It is given that mean and standard deviation are 63,000 and 5,800, respectively.By using central lim...

Q: Please show TI 84 steps. Part d

A: a)t>2.718, df = 11=0.01( From Excel =T.DIST.RT(2.718,11))type error = significance level = 0.01re...

Q: College Units Frequency 0-24 25-49 3 Find the standard deviation for the grouped data. 50-74 6 75-99...

A: The standard deviation for the grouped data is calculations tabulated below: