Question

In: Statistics and Probability

According to a study done by UCB students, the height for Martian adult males is normally...

According to a study done by UCB students, the height for Martian adult males is normally distributed with an average of 64 inches and a standard deviation of 2.3 inches. Suppose one Martian adult male is randomly chosen. Let X = height of the individual. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X ~ N( , ) b. Find the probability that the person is between 59.5 and 62.7 inches. c. The middle 20% of Martian heights lie between what two numbers? Low: inches High: inches?

Solutions

Expert Solution

Solution :

Given that ,

mean =   = 64

standard deviation = =2.3

(A)X ~ N( 64, 2.3)

(B)P(59.5< x <62.7 ) = P[(59.5-64) / 2.3< (x - ) / < (62.7-64) / 2.3)]

= P( -1.96< Z <-0.57 )

= P(Z <-0.57 ) - P(Z <-1.96 )

Using z table   

= 0.2843-0.025

probability= 0.2593

(C)

middle 20% of score is

P(-z < Z < z) = 0.20

P(Z < z) - P(Z < -z) = 0.20

2 P(Z < z) - 1 = 0.20

2 P(Z < z) = 1 + 0.20= 1.20

P(Z < z) = 1.20 / 2 = 0.6

P(Z <0.25 ) = 0.6

z  ± 0.25 using z table

Using z-score formula  

x= z * +

x= -0.25*2.3+64

x= 63.425

Using z-score formula  

x= z * +

x= 0.25*2.3+64

x= 64.575

answer= 63.425 and 64.575


Related Solutions

According to a study done by UCB students, the height for Martian adult males is normally...
According to a study done by UCB students, the height for Martian adult males is normally distributed with an average of 65 inches and a standard deviation of 2.3 inches. Suppose one Martian adult male is randomly chosen. Let X = height of the individual. Round all answers to 3 decimal places where possible. a. What is the distribution of X? X ~ N 65, 2.3 b. Find the probability that the person is between 60.2 and 62.1 inches. 0.0852...
According to a study done by UCB students, the height for Martian adult males is normally...
According to a study done by UCB students, the height for Martian adult males is normally distributed with an average of 65 inches and a standard deviation of 2.4 inches. Suppose one Martian adult male is randomly chosen. Let X = height of the individual. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X ~ N(,) b. Find the probability that the person is between 66.4 and 67.5 inches. c. The middle...
According to a study done by UCB students, the height for Martian adult males is normally...
According to a study done by UCB students, the height for Martian adult males is normally distributed with an average of 65 inches and a standard deviation of 2.5 inches. Suppose one Martian adult male is randomly chosen. Let X = height of the individual. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X ~ N(_,_) b. Find the probability that the person is between 64 and 66.6 inches. c. The middle...
According to a study done by UCB students, the height for Martian adult males is normally...
According to a study done by UCB students, the height for Martian adult males is normally distributed with an average of 65 inches and a standard deviation of 2.5 inches. Suppose one Martian adult male is randomly chosen. Let X = height of the individual. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X ~ N(,) b. Find the probability that the person is between 61.6 and 63.4 inches. c. The middle...
According to a study done by UCB students, the height for Martian adult males is normally...
According to a study done by UCB students, the height for Martian adult males is normally distributed with an average of 68 inches and a standard deviation of 2.4 inches. Suppose one Martian adult male is randomly chosen. Let X = height of the individual. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X ~ N(,) b. Find the probability that the person is between 65.7 and 67.6 inches. c. The middle...
According to a study done by De Anza students, the height for Asian adult males is...
According to a study done by De Anza students, the height for Asian adult males is normally distributed with an average of 66 inches and a standard deviation of 2.5 inches. Suppose one Asian adult male is randomly chosen. Let X = height of the individual. Part B. Find the probability that the person is between 64 and 69 inches. Write the probability statement. What is the probability? (Round your answer to four decimal places.) Sketch the graph. Part C....
Both arm span and height are normally distributed among adult males and females. Most people have...
Both arm span and height are normally distributed among adult males and females. Most people have an arm span approximately equal to their height. This activity will use the data below taken from a spring 2014 Statistics class. Test the claim that the mean arm span is the same as the mean height. Use α= 0.05 as your level of significance. Person # Arm Span (cm) Height (cm) 1 156 162 2 157 160 3 159 162 4 160 155...
The mean height of adult males in the U.S is about 68.8" with a variance of...
The mean height of adult males in the U.S is about 68.8" with a variance of 11.56". Suppose the mean height of a sample of 31 mentally disabled males was found to be 67.3". Researchers want to know if the height of mentally disabled males differs from the population. What can be concluded with α = 0.01? Compute the appropriate test statistic(s) to make a decision about H0. critical value =   If appropriate, compute the CI. If not appropriate, input...
2. It is estimated that the standard deviation of the height of American adult males is...
2. It is estimated that the standard deviation of the height of American adult males is 4 inches. Suppose we survey a sample of 50 men and find a sample mean of 69 inches. (a) For a confidence level of %90, what is the margin of error and the confidence interval? (b) For a confidence level of %95, what is the margin of error and the confidence interval? (c) If we sample 500 men instead, and still insist on %90...
according to a study done by Oxford research Center, 39% of adult americans believe that relationships...
according to a study done by Oxford research Center, 39% of adult americans believe that relationships is now out of date. Suppose a random sample of 500 adult english individuals is asked whether relationships is out of date. A.) what is probability that in a random sample of 500 adult english individauls at most 200 believe that relationships is out of date? B.) What is the probability that in a random sample of 500 adult english individuals between 40% and...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT