Plzz help will give branlisest

An educational psychologist wishes to know the mean number of words a third grader can read per minute. She wants to make an est

zhannawk [14.2K]

Answer:

99% confidence interval for the mean number of words a third grader can read per minute is [24.7 , 25.1].

Step-by-step explanation:

We are given that an educational psychologist wishes to know the mean number of words a third grader can read per minute. She wants to make an estimate at the 99% level of confidence. For a sample of 4657 third graders, the mean words per minute read was 24.9. Assume a population standard deviation of 5.7.

So, the pivotal quantity for 99% confidence interval for the mean number of words a third grader can read per minute is given by;

P.Q. = $\frac{\bar X - \mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\bar X$ = sample mean words per minute read = 24.9

$\sigma$ = population standard deviation = 5.7

n = sample of third graders = 4657

$\mu$ = population mean

So, 99% confidence interval for the population mean, $\mu$ is ;

P(-2.5758 < N(0,1) < 2.5758) = 0.99

P(-2.5758 < $\frac{\bar X - \mu}{\frac{\sigma}{\sqrt{n} } }$ < 2.5758) = 0.99

P( $-2.5758 \times {\frac{\sigma}{\sqrt{n} } }$ < ${\bar X - \mu}$ < $2.5758 \times {\frac{\sigma}{\sqrt{n} } }$ ) = 0.99

P( $\bar X-2.5758 \times {\frac{\sigma}{\sqrt{n} } }$ < $\mu$ < $\bar X+2.5758 \times {\frac{\sigma}{\sqrt{n} } }$ ) = 0.99

99% confidence interval for $\mu$ = [ $\bar X-2.5758 \times {\frac{\sigma}{\sqrt{n} } }$ , $\bar X+2.5758 \times {\frac{\sigma}{\sqrt{n} } }$ ]

= [ $24.9-2.5758 \times {\frac{5.7}{\sqrt{4657} } }$ , $24.9+2.5758 \times {\frac{5.7}{\sqrt{4657} } }$ ]

= [24.7 , 25.1]

Therefore, 99% confidence interval for the mean number of words a third grader can read per minute is [24.7 , 25.1].

6 0

3 years ago

Reduce your answer to its lowest term 2 1/5 + 5 4/5=

elena55 [62]

Answer:

8

Step-by-step explanation:

First you make 2 1/5 11/5

then you make 5 4/5 29/5

then you add them 40/5

40/ 5 simplifiyed is 8

6 0

4 years ago

Read 2 more answers

Is (3, 8) a solution to the equation y = 2x - 1? Explain your answer.

Studentka2010 [4]

Answer:im new how does this work??

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

Need help with this thanks

PolarNik [594]

Step-by-step explanation:

the answer is in the picture above

3 0

3 years ago

In the Ardmore Hotel, 20 percent of the guests (the historical percentage) pay by American Express credit card. (a) What is the

xxMikexx [17]

Answer:

(a) The expected number of guests until the next one pays by American Express credit card is 4.

(b) The probability that the first guest to use an American Express is within the first 10 to checkout is 0.0215.

Step-by-step explanation:

The random variable X can be defined as the number of guests until the next one pays by American Express credit card

The probability that a guest paying by American Express credit card is, p = 0.20.

The random variable X follows a Geometric distribution since it is defined as the number of trials before the first success.

The probability mass function of X is:

$P(X=x)=(1-p)^{x}p;\ x=0,1,2,3...,\ 0$

(a)

The expected value of a Geometric distribution is:

$E(X)=\frac{1-p}{p}$

Compute the expected number of guests until the next one pays by American Express credit card as follows:

$E(X)=\frac{1-p}{p}$

$=\frac{1-0.20}{0.20}$

$=4$

Thus, the expected number of guests until the next one pays by American Express credit card is 4.

(b)

Compute the probability that the first guest to use an American Express is within the first 10 to checkout as follows:

$P(X=10)=(1-0.20)^{10}\times0.20$

$=0.1073741824\times 0.20\\=0.02147483648\\\approx0.0215$

Thus, the probability that the first guest to use an American Express is within the first 10 to checkout is 0.0215.

3 0

4 years ago