Aresearcher collects a simple random sample of grade-point averages of statistics students, and she calculates the mean of this sample. under what conditions can that sample mean be treated as a value from a population having a normal distribution? select all that apply.

a. the sample has more than 30 grade-point averages.

b. if the population of grade-point averages has a normal distribution

c. the researcher collects more than 30 samples.

d. if the population of statistics students has a normal distribution.

A. The sample has more than 30 grade-point averages.

B. If the population of grade-point averages has a normal distribution

Step-by-step explanation:

According to the Central Limit Theorem, if the sample size is big enough(>30) and the population distribution is normal (population of grade point averages) then that sample mean be treated as a value from a population.

Population of statistics students is out of concern in this context since grade-point averages are sampled.

c. 65°

step-by-step explanation:

we are given a triangle with two known angles, 62° and 53°, while the third angle x is unknown and we are to find its value.

we know that the sum of angles in a triangle is equal to a total of 180 degrees. so we can write it as:

x + 62° + 53° = 180°

solving to find the value of x:

x = 180 - (62 + 53) = 65°

therefore, the value of x in this triangle is 65°.

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'.