Question

7. For a standard normal distribution, find:

P(z < c) = 0.1164

Find c rounded to two decimal places.

8.For a standard normal distribution, find:

P(z > c) = 0.89

Find c rounded to two decimal places

9.About ___% of the area under the curve of the standard normal distribution is between z=-0.426 and z=0.426 (or within 0.426 standard deviations of the mean).

10.About ___% of the area under the curve of the standard normal distribution is outside the interval z=[-3.17,3.17] (or beyond 3.17 standard deviations of the mean).

12.A manufacturer knows that their items have a normally distributed lifespan, with a mean of 6.2 years, and standard deviation of 1.1 years.

If you randomly purchase one item, what is the probability it will last longer than 3 years?

14.A particular fruit's weights are normally distributed, with a mean of 399 grams and a standard deviation of 18 grams.

The heaviest 11% of fruits weigh more than how many grams?

Give your answer to the nearest gram.

Answer 1

We need to find z such that P(Z< z)= 0.1164 =z=-1.19 (Normal table) We need to find z such that P(Z > z)= 0.89 =P(Z < z) = 1-0.89 = 0.11 => z= -1.23 (Normal table)

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