Question

) The breaking strength of plastic bags used for packaging produce is normally distributed, with a mean of 17 pounds per square inch and a standard deviation of 9.5 pounds per square inch. What proportion of the bags have a breaking strength of a. less than 14.17 pounds per square inch? _______ b. at least 13.6 pounds per square inch? _______ c. 95% of the breaking strengths will be between what two values symmetrically distributed around the mean? _______ _______ d. less than 13.6 or more than 16.4 _______ e. less than 15 and less than 13.6 f. between 13.6 and 15

Answer 1

Mean = = 17

Standard deviation = = 9.5

a)

We have to find P(X < 14.17)

For finding this probability we have to find z score.

That is we have to find P(Z < - 0.30)

P(Z < - 0.30) = 0.3829

( From z table)

b) We have to find P(X 13.6)

For finding this probability we have to find z score.

That is we have to find P(Z - 0.36)

P(Z - 0.36) = 1 - P(Z < - 0.36) = 1 - 0.3602 = 0.6398

( From z table)

c)

About 95% data lies in the 2 standard deviation from the mean.

That is in the interval

d)

We have to find P(X < 13.6 or X > 16.4)

P(X < 13.6 or X > 16.4) = P(X < 13.6) + P(X > 16.4)

For finding this probability we have to find z score.

P(Z < - 0.36) = 0.3602

P(Z > - 0.06) = 1 - P(Z < - 0.06) = 1 - 0.4748 = 0.5252

P(X < 13.6 or X > 16.4) = P(X < 13.6) + P(X > 16.4) = 0.3602 + 0.5252 = 0.8854

( From z table)

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