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yaroslaw [1]
3 years ago
14

The average score of all golfers for a particular course has a mean of 70and a standard deviation of 5.Suppose 100golfers played

the course today. Find the probability that the average score of the 100golfers exceeded 71.Round to four decimal places.
Mathematics
1 answer:
Schach [20]3 years ago
6 0

Answer:

0.9773

Step-by-step explanation:

Here, we start by calculating the z-scores statistic

Mathematically;

z-score = (x-mean)/SD/√n

From the question, we have;

x = 71, mean = 70, SD = 5 and n = 100

Plugging these values in the equation above, we have;

z-score = (71-70)/5/√100 = 1/5/10 = 1/0.5 = 2

So the probability we want to calculate is that;

P(z > 2)

This is obtainable from the standard normal distribution table

P(z > 2) = 0.97725 which is 0.9773 to 4 decimal places

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A medical researcher wondered if there is a significant difference between the mean birth weight of boy and girl babies. Random
Yuliya22 [10]

Answer:

b) independent samples t-test

t=\frac{(5.92 -5.74)-(0)}{\sqrt{\frac{1.88^2}{5}}+\frac{1.81^2}{5}}=0.154  

p_v =2*P(t_{8}>0.154) =0.881  

So with the p value obtained and using the significance level given \alpha=0.05 we have p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the mean of the group 1 (boys) is NOT significantly different than the mean for the group 2 (Girls).  

Step-by-step explanation:

The system of hypothesis on this case are:  

Null hypothesis: \mu_1 = \mu_2  

Alternative hypothesis: \mu_1 \neq \mu_2  

Or equivalently:  

Null hypothesis: \mu_1 - \mu_2 = 0  

Alternative hypothesis: \mu_1 -\mu_2\neq 0  

Our notation on this case :  

n_1 =5 represent the sample size for group 1  

n_2 =5 represent the sample size for group 2  

We can calculate the mean and deviation for eaach group with the following formulas:

\bar X= \frac{\sum_{i=1}^n X_i}{n}

s = \sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}

\bar X_1 =5.92 represent the sample mean for the group 1  

\bar X_2 =5.74 represent the sample mean for the group 2  

s_1=1.88 represent the sample standard deviation for group 1  

s_2=1.81 represent the sample standard deviation for group 2  

If we see the alternative hypothesis we see that we are conducting a bilateral test and with independnet samples t test.

b) independent samples t-test

The statistic is given by this formula:  

t=\frac{(\bar X_1 -\bar X_2)-(\mu_{1}-\mu_2)}{\sqrt{\frac{s^2_1}{n_1}}+\frac{S^2_2}{n_2}}  

And now we can calculate the statistic:  

t=\frac{(5.92 -5.74)-(0)}{\sqrt{\frac{1.88^2}{5}}+\frac{1.81^2}{5}}=0.154  

The degrees of freedom are given by:  

df=5+5-2=8

And now we can calculate the p value using the altenative hypothesis:  

p_v =2*P(t_{8}>0.154) =0.881  

So with the p value obtained and using the significance level given \alpha=0.05 we have p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the mean of the group 1 (boys) is NOT significantly different than the mean for the group 2 (Girls).  

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Answer:

C

Step-by-step explanation:

given the fact that the other side measures all multiply by 4 when they are enlarged in the second shape, we know that the scale factor is 4. 3 enlarged by a scale factor of 4 = 12

4 0
3 years ago
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In the triangle below, what is the measure of ZC?
Diano4ka-milaya [45]

Answer:

C

Step-by-step explanation:

The triangle is an equilateral triangle, which is equal on all three sides in both side length and angle. since one of them of 60 degrees, then all of them would also be 60 degrees. Since the total amount of degrees in a triangle is 180, 60*3=180 so the answer is C.

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Answer:

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Step-by-step explanation:

(1-15%)a=300

a=255

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Which expression is not equivalent to 2/3 x4
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Answer:

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Step-by-step explanation:

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