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Darina [25.2K]
3 years ago
14

Can you help me with the problem listed in the pictures below? Please and thank you. Will mark BRAINLIEST!!! :)

Mathematics
1 answer:
vagabundo [1.1K]3 years ago
6 0

Answer:

14 books

Step-by-step explanation:

Let b = number of books at the beginning

She sold 1/2 of the books

b - 1/2 b

This is how many she had left

Then she bought 7

b - 1/2 b + 7

this equals 14

b - 1/2 b + 7 = 14

Combine like terms

1/2 b + 7 = 14

Subtract 7 from each side

1/2 b = 14-7

1/2 b = 7

Multiply each side by 2

1/2 b * 2 = 7*2

b = 14

She started with 14 books

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Answer:

a) 0.0304 = 3.04% probability a randomly chosen apple exceeds 100 g in weight.

b) The weight that 80% of the apples exceed is of 78.28g.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Weights of apples are normally distributed with a mean of 85 grams and a standard deviation of 8 grams.

This means that \mu = 85, \sigma = 8

a. Find the probability a randomly chosen apple exceeds 100 g in weight.

This is 1 subtracted by the p-value of Z when X = 100. So

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

Z = \frac{100 - 85}{8}

Z = 1.875

Z = 1.875 has a p-value of 0.9697

1 - 0.9696 = 0.0304

0.0304 = 3.04% probability a randomly chosen apple exceeds 100 g in weight.

b. What weight do 80% of the apples exceed?

This is the 100 - 80 = 20th percentile, which is X when Z has a p-value of 0.2, so X when Z = -0.84.

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

-0.84 = \frac{X- 85}{8}

X - 85 = -0.84*8

X = 78.28

The weight that 80% of the apples exceed is of 78.28g.

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