use the number and decimal to write a number in which the digit 2 is one tenth the value of the digit 2 in 8.524

The heights of students at a college are normally distributed with a mean of 175 cm and a standard deviation of 6 cm. One might

frosja888 [35]

Answer:

25

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 175cm

Standard deviation = 6 cm

Percentage of students below 163 cm

163 = 175 - 2*6

So 163 is two standard deviations below the mean.

By the Empirical rule, 95% of the heights are within 2 standard deviations of the mean. The other 100-95 = 5% are more than 2 standard deviations of the mean. Since the normal distribution is symmetric, 2.5% of them are more than 2 standard deviations below the mean(so below 163cm) and 2.5% are more than two standard deviations above the mean.

2.5% of the students have heights less than 163cm.

Out of 1000

0.025*1000 = 25

25 is the answer

8 0

3 years ago

Read 2 more answers

Explain how many cupcakes Jasmine can make if she had 5 1/4 cups of frosting but needs 3/8 cups for each cupcake

kobusy [5.1K]

Answer:

jasmine can make 14 cupcakes

Step-by-step explanation:

5 1/4 = 5.25

3/8 = 0.375

5.25/0.375 = 14

7 0

3 years ago

While her husband spent 2½ hours picking out new speakers, a statistician decided to determine whether the percent of men who en

AVprozaik [17]

Answer:

$z=\frac{p_{M}-p_{W}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{M}}+\frac{1}{n_{W}})}}$ (1)

$z=\frac{0.34848-0.34782}{\sqrt{0.34831(1-0.34831)(\frac{1}{66}+\frac{1}{23})}}=0.0057$

$p_v =P(Z>0.0057)=0.4977$

The p value is a very high value and using the significance level $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say the the percent of men who enjoy shopping for electronic equipment is NOT significantly higher than the percent of women who enjoy shopping for electronic equipment.

Step-by-step explanation:

1) Data given and notation

$X_{M}=23$ represent the number of men that said they enjoyed the activity of Saturday afternoon shopping

$X_{W}=8$ represent the number of women that said they enjoyed the activity of Saturday afternoon shopping

$n_{M}=66$ sample of male selected

$n_{W}=23$ sample of demale selected

$p_{M}=\frac{23}{66}=0.34848$ represent the proportion of men that said they enjoyed the activity of Saturday afternoon shopping

$p_{W}=\frac{8}{23}=0.34782$ represent the proportion of women with red/green color blindness

z would represent the statistic (variable of interest)

$p_v$ represent the value for the test (variable of interest)

2) Concepts and formulas to use

We need to conduct a hypothesis in order to check if the percent of men who enjoy shopping for electronic equipment is higher than the percent of women who enjoy shopping for electronic equipment , the system of hypothesis would be:

Null hypothesis: $p_{M} \leq p_{W}$

Alternative hypothesis: $p_{M} > p_{W}$

We need to apply a z test to compare proportions, and the statistic is given by:

$z=\frac{p_{M}-p_{W}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{M}}+\frac{1}{n_{W}})}}$ (1)

Where $\hat p=\frac{X_{M}+X_{W}}{n_{M}+n_{W}}=\frac{23+8}{66+23}=0.34831$

3) Calculate the statistic

Replacing in formula (1) the values obtained we got this:

$z=\frac{0.34848-0.34782}{\sqrt{0.34831(1-0.34831)(\frac{1}{66}+\frac{1}{23})}}=0.0057$

4) Statistical decision

Using the significance level provided $\alpha=0.05$ , the next step would be calculate the p value for this test.

Since is a one side right tail test the p value would be:

$p_v =P(Z>0.0057)=0.4977$

So the p value is a very high value and using the significance level $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say the the percent of men who enjoy shopping for electronic equipment is NOT significantly higher than the percent of women who enjoy shopping for electronic equipment.

4 0

3 years ago

The composite figure is made up of a triangular prism and a pyramid. The two solids have congruent bases.

kolezko [41]

The correct question is
The composite figure is made up of a triangular prism and a pyramid. The two solids have congruent bases. What is the volume of the composite figure<span>?
</span>
the complete question in the attached figure

we know that
[volume of a cone]=[area of the base]*h/3
[area of the base]=22*10/2-------> 110 units²
h=19.5 units
[volume of a cone]=[110]*19.5/3------> 715 units³

[volume of a triangular prism]=[area of the base]*h
[area of the base]=110 units²
h=25 units
[volume of a a triangular prism]=[110]*25------------> 2750 units³

[volume of a the composite figure]=[volume of a cone]+[volume of a <span>a triangular prism]

</span>[volume of a the composite figure]=[715]+[2750]-------> 3465 units³

the answer is
The volume of a the composite figure is 3465 units³

4 0

3 years ago

Read 2 more answers

A pole-vaulter uses a 15-foot-long pile. She grips the pole so that the segment below her left hand is twice the length of the s

Shalnov [3]

Let x + 1.5 be length of segment above left hand
Let 2x be length of segment below left hand

15 = x + 1.5 + 2x
15 = 3x + 1.5
15 - 1.5 = 3x
13.5 = 3x
13.5/3= 3x/3
4.5 = x
x = 4.5
This is the length above the left hand.

2x must be then 4.5*2 = 9 foot
This is the length below the left hand.

Checking
4.5 + 9 + 1.5 = 15 foot

Adding length below left hand & length of left hand to right hand:
9 + 1.5 = 10.5
The right hand is hence 10.5 foot far up the pole.

6 0

3 years ago