The population of measurements is approximately normal, with mean 37 cm and standard deviation 5 cm. Suppose that a sample of size 10 is randomly selected from this population. What is the probability that all 10 have a calf circumference greater than 42 cm? Now suppose that a sample of size 10 is randomly selected from the population described in problem 9. What is the probability that the average of the 10 measurements is greater than 42 cm?

a) 0.1587

b) 0.0008

Step-by-step explanation:

Given that:

Mean (m) = 37 cm

Sample size (n) = 10

standard deviation (s) = 5 cm

a) the z score (z) =

where x = 42 cm

Therefore,

The probability that all 10 have a calf circumference greater than 42 cm =

P(x > 42) = P (z > 1) = 1 - P(z < 1) = 1 - 0.8413 = 0.1587

b) The standard error of the mean is a measure of how far that the sample mean will be from the population mean for a repeated random samples of size n.

The standard error of the mean (e)= s /√n

e = s /(√n ) = 5 / (√10)  = 1.5811

The z score (z) =

where x = 42 cm

Therefore,

P(x > 42) = P (z > 3.16) = 1 - P(z < 3.16) = 1 - 0.9992 = 0.008

answer: given that the roller coaster can accommodate 1600 riders per hour, thus the roller coaster can accomodate 1600 / 60 = 26.67 riders per minute.

given that there are 345 people in the line, the number of minutes it will take for the 345 persons to get into the roller coaster is given by 345 / 26.67 = 12.94 minutes.

therefore, it will take you 12.94 minutes to get to the front of the line.

step-by-step explanation:

no association

step-by-step explanation:

if you have eyes and you can use them efficiently you can see that it just looks like random dots like do a line of best fit and like they're so spread out it's such a weak association you might as well consider it nonexistent