Question

In: Math

3. The heights of female students attending a sixth form college have a mean of 168...

3. The heights of female students attending a sixth form college have a mean of 168 cm and standard deviation of 4.5 cm. The heights can be modeled by a normal distribution: a. Find the probability that the height of a randomly selected female student attending this college is less than 172.5 cm? b. Find the probability that the mean height of a random sample of 11 female students from this college exceeds 172 cm?

Solutions

Expert Solution

Solution:

Given: The heights of female students attending a sixth form college follows a Normal distribution with a mean of 168 cm and a standard deviation of 4.5 cm.

That is:  

Part a) Find the probability that the height of a randomly selected female student attending this college is less than 172.5 cm.

That is find:

P( X < 172.5 ) =..........?

Find z score for x = 172.5

Thus we get:

P( X < 172.5 ) =P( Z< 1.00)

Look in z table for z= 1.0 and 0.00 and find corresponding area.

P(Z < 1.00) = 0.8413

Thus

P( X < 172.5 ) =P( Z< 1.00)

P( X < 172.5 ) =0.8413

Thus the probability that the height of a randomly selected female student attending this college is less than 172.5 cm is 0.8413

Part b) Find the probability that the mean height of a random sample of 11 female students from this college exceeds 172 cm

Sample size = n = 11

That is find :

Use following z score formula for sample mean.

Thus we get:

Look in z table for z = 2.9 and 0.05 and find corresponding area.

P( Z < 2.95 ) = 0.9984

Thus

Thus the probability that the mean height of a random sample of 11 female students from this college exceeds 172 cm is 0.0016


Related Solutions

Consider the approximately normal population of heights of female college students with a mean μ =...
Consider the approximately normal population of heights of female college students with a mean μ = 69.5 inches and a standard deviation σ = 3 inches. A random sample of 36 females is obtained. a. What is the probability that an individual height of a female college student, x, is at least 70 inches? Mark and label the mean μ along with the x value then shade the area defining the probability of interest on the graph A. Mark and...
The figure below shows a frequency and​ relative-frequency distribution for the heights of female students attending...
The figure below shows a frequency and​ relative-frequency distribution for the heights of female students attending a college. Records show that the mean height of these students is 64.564.5 inches and that the standard deviation is 1.81.8 inches. Use the given information to complete parts​ (a) through​ (c). Height​ (in.) Frequency f Relative freq. 60dash–under 61 22 0.00680.0068 61dash–under 62 66 0.02050.0205 62dash–under 63 2929 0.09900.0990 63dash–under 64 6565 0.22180.2218 64dash–under 65 9191 0.31060.3106 65dash–under 66 6969 0.23550.2355 66dash–under 67...
The heights of female students in a university are approx normally distributed with a mean of...
The heights of female students in a university are approx normally distributed with a mean of 162 cm and a standard dev of 8 cm. Explain your answers. a) Approx 68% of all female students in a university will have heights between ____ cm and ____ cm. b) Heights greater than ____ cm would be considered peculiar.
The heights of 500 female students, half of whom are college students while the other half are second-grade students.
The heights of 500 female students, half of whom are college students while the other half are second-grade students.Describing Distributions. For each distribution described in Exercises, answer the following questions:a. How many modes would you expect for the distribution?b. Would you expect the distribution to be symmetric, left skewed, or right-skewed?
1. Assume that female students’ heights are normally distributed with a mean given by µ =...
1. Assume that female students’ heights are normally distributed with a mean given by µ = 64.2 in. and a standard deviation given by σ =2.6 in. a) If one female student is randomly selected, find the probability that her height is between 64.2 in. and 66.2 in. b) If 25 female students are randomly selected, find the probability that they have a mean height between 64.2 in. and 66.2 in.
The heights of female students at a university follows Normal distribution with a mean 66 inches...
The heights of female students at a university follows Normal distribution with a mean 66 inches and a standard deviation 3 inches. A researcher randomly selects 36 female students from the university, surveys their heights and calculates a sample mean. Now suppose that the population standard deviation is unknown. Also, the researcher calculate the sample standard deviation to be 3 inches. a) What is the probability that the sample mean height is between 65 inches and 67 inches? b) Instead...
Assume that female students’ heights are normally distributed with a mean given by µ = 64.2...
Assume that female students’ heights are normally distributed with a mean given by µ = 64.2 in. and a standard deviation given by σ =2.6 in. a) If one female student is randomly selected, find the probability that her height is between 64.2 inches and 66.2 inches b) If 25 female students are randomly selected, find the probability that they have a mean height between 64.2 inches and 66.2 inches
) Suppose College male students’ heights are normally distributed with a mean of µ = 69.5...
) Suppose College male students’ heights are normally distributed with a mean of µ = 69.5 inches and a standard deviation of σ =2.8 inches. What is the probability that randomly selected male is at least 70.5 inches tall? If one male student is randomly selected, find the probability that his height is less than 65.2 inches or greater than 71.2 inches. How tall is Shivam if only 30.5% of students are taller than him There are 30.5% of all...
Consider the approximately normal population of heights of male college students with mean μ = 68...
Consider the approximately normal population of heights of male college students with mean μ = 68 inches and standard deviation of σ = 4.6 inches. A random sample of 13 heights is obtained. (b) Find the proportion of male college students whose height is greater than 71 inches. (Round your answer to four decimal places.) e) Find P(x > 71). (Round your answer to four decimal places.) (f) Find P(x < 70). (Round your answer to four decimal places.)
Consider the approximately normal population of heights of male college students with mean μ = 72...
Consider the approximately normal population of heights of male college students with mean μ = 72 inches and standard deviation of σ = 8.2 inches. A random sample of 12 heights is obtained. (a) Describe the distribution of x, height of male college students. skewed right, approximately normal, skewed left (b) Find the proportion of male college students whose height is greater than 74 inches. (Give your answer correct to four decimal places.) (c) Describe the distribution of x, the...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT