Question

Asked Oct 24, 2019

Step 1

a)

The probability that a randomly selected item is between 27.5 and 40.6 is obtained below:

The value of mean μ = 32.9 and standard deviation is 35.2

The following normal curve corresponds to *P* (27.5 ≤ *X* ≤ 40.6) is obtained below:

The *P* (27.5 ≤ *X* ≤ 40.6) is developed using MINITAB**:**

- Choose
**Graph > Probability Distribution Plot**choose**View Probability****> OK.** - From
**Distribution**, choose ‘**Normal**’ distribution. - In
**Mean**enter the value as 32.9. - In
**Standard deviation**enter the value as 35.2. - Click the
**Shaded Area** - Choose
and*X*Value**Middle**for the region of the curve to shade. - Enter the
**X value 1**as**27.5**. - Enter the
**X value 2**as**40.6**. - Click
**OK**.

Follow the above instructions to obtain the MINITAB output.

Step 2

From the MINITAB output the value of *P* (27.5 ≤ *X* ≤ 40.6) is 0.1475.

(b)

The probability that a sample size 25 is randomly selected and is less than 28.2 is obtained below:

By central limit theorem, the sample size is 25 with mean μ = 32.9 and standard deviation, 35.2 /sqrt (25) = 7.04.

The following normal curve corresponds to *P* (X < 28.2) is obtained below:

The *P* (X < 28.2) is developed using MINITAB**:**

- Choose
**Graph > Probability Distribution Plot**choose**View Probability****> OK.** - From
**Distribution**, choose ‘**Normal**’ distribution. - In
**Mean**enter the va...

Tagged in

Q: If P(B) = 0.3, P(A or B)= .06, and P(A and B)= .2, find P(A)

A: From the properties of probability, for any two events A and B we have

Q: Harley-Davidson motorcycles make up 14% of all the motorcycles registered in the United States. You ...

A: It is given that, Harley-Davidson motor cycle make up 14% of the motor cycles registered in US. That...

Q: 8.5.49-BE Question Help The annual premium for a $10,000 insurance policy against the theft of a pai...

A: Expected value:Consider the event 1 as the paint will be stolen and the event 2 as the paint will no...

Q: Larry, Kim , Jim, Ian, and Simone have all been invited to a dinner party. They arrive randomly and ...

A: Factorial of an integer:The factorial of an integer is the product of all positive integers less tha...

Q: An urn contains 5 red, 6 blue, and 8 green balls. If a set of 3 balls is randomly selected, what is ...

A: Sampling without replacement:The urn consists of 19 balls in total. The sampling is done with replac...

Q: A standard deck of 52 cards has four suits (hearts, diamonds, clubs,and spades). Each suit has thirt...

A: To calculate the probability of the required events , counting the number of outcomes in each case

Q: Phil Dunphy, a real estate agent, is considering whether he should list an unusual $372,875 house fo...

A: Expected value:The expected value of a random variable is the sum of the possible values that the ra...

Q: 5.80 but use 5.79 as a reference

A: Consider,D be the event that shows an odd sum on rolling of two dice.B be the event that denotes a s...

Q: In a survey of consumers aged 12 and older, respondents were asked how many cell phones were in use...

A: Click to see the answer