Suppose a population has a mean happiness score of 75 and a standard deviation of 15. Researcher A takes a random sample of 100 participants. Researcher B takes a random sample of 25 participants. Which researcher is more likely to get a sample mean of 80 or higher

Researcher A is more likely to get a sample mean of 80 or higher

Step-by-step explanation:

The central limit theorem states that if the sample size increases the sampling distribution of the mean approaches normal distribution.The z score would be given by

z= x`- ux/ (σx/√n)

The sample standard deviation is given by  15 / √25 = 3 and  15 / √100 = 1.5

z=75-ux/3/5

Suppose z= 1.96

1.96 = 75 - ux /0.6

1.176- 75= -ux

ux = 73.824

Now Putting values for the second sample

z=75-ux/1.5/10

Suppose z= 1.96

1.96 = 75 - ux /0.15

0.2904- 75= -ux

ux = 74.706

From the above we see that the larger sample size would give a sample mean  equal to the population mean .

d. millimeters per hour.

step-by-step explanation:

we are given that,

carlo used a rain gauge to measure the amount of water his lawn is receiving from the sprinklers.

since, according to the options, we see that,

water cannot be measured by 'miles per hour', 'meters per second' and 'grams per seconds'.

we get that, the water can be measured by 'millimeters per hour'.

hence, the appropriate rate for describing the amount of water is 'millimeters per hour'.

step-by-step explanation:

in which figure is point g a centroid