Question

The diameters of ball bearings are distributed normally. The mean diameter is 96 millimeters and the standard deviation is 6 millimeters.

Find the probability that the diameter of a selected bearing is between 89 and 105 millimeters. Round your answer to four decimal places.

Answer #1

We need to find the P(89<x<105)

We need to identify the z-value for each of this condition as the distribution is normal. Z value is given as (x-mean)/(Standard deviation)

From normal tables we know that P(z<1.5) = 0.9332

From normal tables we know that P(-1.667<z) = 1-P(z<1.667) = 1-0.878 = 0.1217

Hence required probability is 0.9332-0.1217 = 0.8115

**Hence the probability that
the diameter of a selected bearing is between 89 and 105
millimeters is 0.8115**

The diameters of ball bearings are distributed normally. The
mean diameter is 89 millimeters and the variance is 9. Find the
probability that the diameter of a selected bearing is between 83
and 91 millimeters. Round your answer to four decimal
places.

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mean diameter is 125 millimeters and the standard deviation is 3
millimeters. Find the probability that the diameter of a selected
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decimal places.

The diameters of ball bearings are distributed normally. The
mean diameter is 106 millimeters and the standard deviation is 4
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The diameters of ball bearings are distributed normally. The
mean diameter is 120120 millimeters and the standard deviation is
44 millimeters. Find the probability that the diameter of a
selected bearing is greater than 125125 millimeters. Round your
answer to four decimal places.

The diameters of ball bearings are distributed normally. The
mean diameter is 120 millimeters and the standard deviation is 4
millimeters. Find the probability that the diameter of a selected
bearing is greater than 125 millimeters. Round your answer to four
decimal places.

The diameters of ball bearings are distributed normally. The
mean diameter is 135millimeters and the variance is 9. Find the
probability that the diameter of a selected bearing is between 137
and 139millimeters. Round your answer to four decimal places.

A process manufactures ball bearings with diameters that are
normally distributed with mean 25.1 millimeters and standard
deviation 0.08 millimeter.
(a) What proportion of the diameters are less than 25.0
millimeters?
(b) What proportions of the diameters are greater than 25.4?
(c) To meet a certain specification, a ball bearing must have a
diameter between 25.0 and 25.3 millimeters. What proportions of the
ball bearings meet specification?
(d) Find the 95th percentile of the diameters.

Precision manufacturing: A process manufactures ball bearings
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(c) To meet a certain specification, a ball bearing must have a
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0.782 inch and a standard deviation of 0.008 inch. Complete
parts (a) through (e) below.
a. What is the probability that a ball...

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