Question

Asked Oct 23, 2019

he mean of a normal probability distribution is 60; the standard deviation is 5.

a. About what percent of the observations lie between 55 and 65?

b. About what percent of the observations lie between 50 and 70?

c. About what percent of the observations lie between 45 and 75? (Round your answers to 1 decimal place.)

Step 1

Given mean of the normal distribution = 60

Standard deviation = 5

The Z score of 55 and 65 are calculated as shown below, we get Z scores as -1 and 1 respectively

Step 2

With respect to below mentioned z tables P(Z ≤ -1) = 0.1587 and P( Z ≤ 1) = 0.8413

P(-1 ≤ Z ≤ 1) = P(Z ≤ 1) - P(Z ≤ -1) = 0.8413 - 0.1587 = 0.6826

The percentage of observations between 55 and 65 is 68.3 % (rounded to 1 decimal)

Step 3

The Z score of 50 and 70 are calculated as shown below,...

Tagged in

Q: The lifetime of a particular component is normally distributed with a mean of 1000 hours and a stand...

A: Introduction:Let X denotes the lifetime of a particular component is normally distributed with mean ...

Q: A pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan i...

A: The probability that this whole shipment will be accepted is obtained below:Here, the rates of defec...

Q: I need help understanding how to solve b-d. I'm confused as to how they equal different solutions.

A: b.Here the total number of persons belongs to S1, n(S1) is 194.The total number of persons who belon...

Q: Explain how a “distribution of means” is created and when it is appropriate as the “comparison distr...

A: When you draw infinite random samples of a given size from a population with replacement, the means ...

Q: n a test of H0: p = 0.4 against H1: p ≠ 0.4, a sample of size 100 produces Z = 1.28 for the value of...

A: The p-value (or observed level of significance) of the test is approximately equal to is,Step-by-ste...

Q: Golden Retriever German Short Hair Pointer 3 Begian Tervuren 1 Australian Shepherd 3 Border Collie 1...

A: Given data and calculation of relative frequency is shown in the table

Q: Alice owns a snow shoveling business. For each driveway, she charges $50 plus $70 per hour of work. ...

A: Independent and dependent variables in regression:In a simple regression, the variable of interest, ...

Q: Scores on a certain test are normally distributed with a variance of 70. A researcher wishes to esti...

A: From the given information, the confidence level is 0.95, the variance is 70 and the margin of error...

Q: An independent-measures study with n = 6 in each sample produces a sample mean difference of 4 point...

A: The provided information is: