1. Triangle ABC is congruent to triangle EDF. So, Kiran knows that there is a sequence of rigid motions that takes ABC to EDF.

We have been given for a normal distribution the mean time it takes to walk to the bus stop is 8 minutes with a standard deviation of 2 minutes. And the mean time it takes for the bus to get to school is 20 minutes with a standard deviation of 4 minutes.

(a) Average time that it would take reach school can be obtained by adding the average times.

8+20 = 28 minutes.

(b) Standard deviation of the trip to school can be found as:

$\sigma =\sqrt{2^{2}+4^{2}}=\sqrt{4+16}=\sqrt{20}=4.47$

Therefore, standard deviation of the entire trip is 4.47 minutes.

(c) Let us first find z score corresponding to 30 minutes. $z=\frac{x-\mu }{\sigma }=\frac{30-28}{4.47}=0.447$

We need to find the probability such that $P(x>30)=P(z>0.447)=0.67$

Therefore, the required probability is 0.67.

(d) If average time to walk to school is 10 minutes, then overall average time for the trip will be 10+20 = 30 minutes.

(e) Standard deviation won't change it will remain 4.47

(f) The new probability will be:

$z=\frac{x-\mu }{\sigma }=\frac{30-90}{4.47}=0$

$P(x>30)=P(z>0)=0.5$

Therefore, probability will be 0.50.

6 0

3 years ago

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37% of women consider themselves fans of professional baseball. you randomly select six women and ask each if she considers hers

valina [46]

Answer:

(a) 2.22

(b) 1.3986

(c) 1.183

Step-by-step explanation:

Let X denote the number of women who consider themselves fans of professional baseball.

The proportion of women who consider themselves fans of professional baseball is, p = 0.37.

A random sample of n = 6 women are selected and each was asked if she considers herself a fan of professional baseball.

Each woman's reply is independent of the others.

The random variable X thus follows a binomial distribution with parameters n = 6 and p = 0.37.

(a)

Compute the mean of the binomial distribution as follows:

$\text{Mean}=np=6\times 0.37=2.22$

(b)

Compute the variance of the binomial distribution as follows:

$\text{Variance}=np(1-p)=6\times 0.37\times (1-0.37)=1.3986$

(c)

Compute the standard deviation of the binomial distribution as follows:

$\text{Standard Deviation}=\sqrt{np(1-p)}=\sqrt{6\times 0.37\times (1-0.37)}=1.183$

5 0

3 years ago