Question

6.5 Given a normal distribution with \( \mu=70 \) and \( \sigma=20 \), what is the probability that a. \( X>110 \). b. \( X<10 \). c. \( X<70 \) or \( X>130 \). d. Between what two \( \mathrm{X} \) values (symmetrically distributed around the mean) are \( 70 \% \) of the values.

          6.5 Given a normal distribution with \( \mu=70 \) and \( \sigma=20 \), what is the probability that
a. \( X>110 \).
b. \( X<10 \).
c. \( X<70 \) or \( X>130 \).
d. Between what two \( \mathrm{X} \) values (symmetrically distributed around the mean) are \( 70 \% \) of the values.

6.5 Given a normal distribution with μ=70 and σ=20, what is the probability that
a. X>110.
b. X<10.
c. X<70 or X>130.
d. Between what two X values (symmetrically distributed around the mean) are 70 % of the values.

Added by Andrew F.

Statistics for Business and Economics

Paul Newbold, William Carlson, Betty… 8th Edition

Chapter 5

Instant Answer

Solved by Expert Willis James

Step 1

The z-score is calculated as \( Z = (X - \mu) / \sigma \). So, \( Z = (110 - 70) / 20 = 2 \). Looking up 2 in the z-table, we find that the probability that Z is less than 2 is 0.9772. But we want the probability that Z is greater than 2, so we subtract the value Show more…

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6.5 Given a normal distribution with \( \mu=70 \) and \( \sigma=20 \), what is the probability that a. \( X>110 \). b. \( X<10 \). c. \( X<70 \) or \( X>130 \). d. Between what two \( \mathrm{X} \) values (symmetrically distributed around the mean) are \( 70 \% \) of the values.