Assume a normal distribution of items with a mean of 100 and a standard deviatio

Question

Assume a normal distribution of items with a mean of 100 and a standard deviation of 10. What is the probability (as a percent with two decimal places) that an item drawn at random is between 87 and 105? Do not show the percent sign. For instance, enter 46.22 if your computed answer is 46.211%.

What is the answer?________________

Assume a normal distribution of items with a mean of 100 and a standard deviation of 10. What is the probability (as a percent with two decimal places) that an item drawn at random is within 5 of the mean? Do not show the percent sign. For instance, enter 46.22 if your computed answer is 46.211%.

What is the answer?_______________

Explanation / Answer

1)

P(87<X<105) = P(X<105) - P(X<87)

= P(Z < 105-100/10) - P(Z< 87-100/10)

= P(Z < 0.5) - P(Z < -1.3)

= 0.6915 - 0.0968

= 0.5947

= 59.47%

P(95 < X < 105) = P(X<105) - P(X<95)

= 0.6915 - 0.3085

= 0.383

= 38.3%

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