In a large school district, it is known that 25% of all students entering kindergarten are already reading. A simple random sample of 10 new kindergarteners is drawn. What is the probability that fewer than three of them are able to read?

A .2503

B .2816

C .5000

D .5256

E .7759

Any formulas or ways to remember when to use a certain formula would be great, seeing as how I forgot how to do this stuff!

Given Information:

Probability of success = p = 25% = 0.25

Number of trials = n = 10   

Required Information:

P(x < 3) = ?

P(x < 3) = 0.5256 (option D)

Step-by-step explanation:

The given problem can be solved using binomial distribution since:

The binomial distribution is given by

P(x) = ⁿCₓ pˣ (1 - p)ⁿ⁻ˣ

Where n is the number of trials, x is the variable of interest and p is the probability of success.

The variable of interest in this case is fewer than 3 students and the probability that fewer than three students are able to read is

P(x < 3) = P(x = 0) + P(x = 1) + P(x = 2)

For P(x = 0):

Here we have x = 0, n = 10 and p = 0.25

P(x = 0) = ¹⁰C₀(0.25⁰)(1 - 0.25)¹⁰⁻⁰

P(x = 0) = (1)(0.25⁰)(0.75)¹⁰

P(x = 0) = 0.0563

For P(x = 1):

Here we have x = 1, n = 10 and p = 0.25

P(x = 1) = ¹⁰C₁(0.25¹)(1 - 0.25)¹⁰⁻¹

P(x = 1) = (10)(0.25¹)(0.75)⁹

P(x = 1) = 0.1877

For P(x = 2):

Here we have x = 2, n = 10 and p = 0.25

P(x = 2) = ¹⁰C₂(0.25²)(1 - 0.25)¹⁰⁻²

P(x = 2) = (45)(0.25²)(0.75)⁸

P(x = 2) = 0.28157

Finally,

P(x < 3) = P(x = 0) + P(x = 1) + P(x = 2)

P(x < 3) = 0.0563 + 0.1877 + 0.28157

P(x < 3) = 0.52557

Rounding off yields

P(x < 3) = 0.5256

Therefore, the probability that fewer than three of the students are able to read is 0.5256

you need a common difference between consecutive terms to be constant, like 1,2,3,4 or 2,4,6,8, or 1,3,6,9

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'.