Select the correct answer from the drop-down menu. The number of books borrowed from a library each week follows a normal distribution. When a sample is taken for several weeks, the mean is found to be 190 and the standard deviation is 30. There is a___ % chance that more than 250 books were borrowed in a week. fill the blank

Question

Alannah

Mathematics

15 March, 07:48

Select the correct answer from the drop-down menu. The number of books borrowed from a library each week follows a normal distribution. When a sample is taken for several weeks, the mean is found to be 190 and the standard deviation is 30. There is a___ % chance that more than 250 books were borrowed in a week. fill the blank

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Answers (2)

Know the Answer?

Kieran Larson · Answer 1

Kieran Larson 15 March, 07:57

0

The answer would be 2.5%

Sneakers · Answer 2

There is a 2.28% chance that more than 250 books were borrowed in a week.

Thus the probability that more than 250 books were borrowed in a week is 0.0228 = 2.28%

Step-by-step explanation:

d) the probability that, on average, the number of books borrowed from the library as a mean of 190 and standard deviation of 30.

The area under part of a normal probability curve is directly proportional to probability and the value is calculated as

z = (x₁-x) / σ

where z = propability of normal curve

x₁ = variate mean = 250

x = mean of 190

σ = standard deviation = 30

applying the formula,

z = (250-190) / 30

z = 60/30 = 2

Using a table of partial areas beneath the standardized normal curve (see Table of normal curve, a z-value of 2 corresponds to an area of 0.4772 between the mean value. but, because the standard curve has 0.5, then will minus 0.4772 from 0.5 = 0.5 - 0.4772 = 0.0228

Thus the probability that more than 250 books were borrowed in a week is 0.0228 = 2.28%