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DiKsa [7]
3 years ago
8

The frequency table was made using a bag containing slips of paper that are numbered 1, 2, 3, 4, or 5.

Mathematics
1 answer:
snow_lady [41]3 years ago
6 0
Probability is given by the formula:
Probability=(number of favorable outcomes)/(Total number of possible outcomes)
thus;
Given that t<span>he frequency table was made using a bag containing slips of paper that are numbered 1, 2, 3, 4, or 5.
then:
1] Probability of obtaining 1
Number of favorable outcome=4
Total number of outcomes=(4+12+20+32+12)=80
P(1)=4/80=0.05

2]Probability of obtaining a 2
Number of favorable outcomes=12
thus
P(2)=12/80=0.15

3] Probability of obtaining a 3
Number of favorable outcomes=20
thus
P(3)=20/80=0.25

4] Probability of obtaining a 4
Number of favorable outcomes=32
thus
P(4)=32/40=0.8

5] Probability of obtaining a 5
Number of favorable outcomes=12
thus
P(5)=12/80=0.15</span>
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The College Boards, which are administered each year to many thousands of high school students, are scored so as to yield a mean
Marysya12 [62]

Answer:

a) 15.87% of the scores are expected to be greater than 600.

b) 2.28% of the scores are expected to be greater than 700.

c) 30.85% of the scores are expected to be less than 450.

d) 53.28% of the scores are expected to be between 450 and 600.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

\mu = 500, \sigma = 100

a. Greater than 600

This is 1 subtracted by the pvalue of Z when X = 600. So

Z = \frac{X - \mu}{\sigma}

Z = \frac{600 - 500}{100}

Z = 1

Z = 1 has a pvalue of 0.8413.

1 - 0.8413 = 0.1587

15.87% of the scores are expected to be greater than 600.

b. Greater than 700

This is 1 subtracted by the pvalue of Z when X = 700. So

Z = \frac{X - \mu}{\sigma}

Z = \frac{700 - 500}{100}

Z = 2

Z = 2 has a pvalue of 0.9772

1 - 0.9772 = 0.0228

2.28% of the scores are expected to be greater than 700.

c. Less than 450

Pvalue of Z when X = 450. So

Z = \frac{X - \mu}{\sigma}

Z = \frac{450 - 500}{100}

Z = -0.5

Z = -0.5 has a pvalue of 0.3085.

30.85% of the scores are expected to be less than 450.

d. Between 450 and 600

pvalue of Z when X = 600 subtracted by the pvalue of Z when X = 450. So

X = 600

Z = \frac{X - \mu}{\sigma}

Z = \frac{600 - 500}{100}

Z = 1

Z = 1 has a pvalue of 0.8413.

X = 450

Z = \frac{X - \mu}{\sigma}

Z = \frac{450 - 500}{100}

Z = -0.5

Z = -0.5 has a pvalue of 0.3085.

0.8413 - 0.3085 = 0.5328

53.28% of the scores are expected to be between 450 and 600.

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2 years ago
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The diameter of the new rubber ball, to the nearest foot, must be D =  4.0 ft (in the case of the maximum cost).

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The sum of the circumference and diameter of a circle is 116 cm. Find its radius
AleksAgata [21]

Answer:

Step-by-step explanation:

A.t.q,

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Thank you

3 0
2 years ago
Read 2 more answers
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