Using the normal distribution, it is found that there is a 0.963 = 96.3% probability that on a given day, his commute will be longer than 49 minutes.
<h3>Normal Probability Distribution</h3>
The z-score of a measure X of a normally distributed variable with mean and standard deviation is given by:
- The z-score measures how many standard deviations the measure is above or below the mean.
- Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.
In this problem, the mean and the standard deviation are given, respectively, by:
.
The probability that on a given day, his commute will be longer than 49 minutes is <u>one subtracted by the p-value of Z when X = 49</u>, hence:
Z = -1.78
Z = -1.78 has a p-value of 0.0375.
1 - 0.0375 = 0.963.
0.963 = 96.3% probability that on a given day, his commute will be longer than 49 minutes.
More can be learned about the normal distribution at brainly.com/question/24663213
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The magnitude of the gravitational force between the two spheres is approximately; F = 1.67 x 10⁻⁹ N
<h3>Gravitational Force</h3>
We are given;
Mass 1; M = 15 kg
Mass 2; m = 15 kg
distance of separation; r = 3 m
Formula for gravitational force using newtons law of gravitation is;
F = GMm/r²
where;
M is mass 1
m is mass 2
G is gravitational constant = 6.67 × 10⁻¹¹ N.kg²/m²
r is distance of separation
Plugging in the relevant values, we have;
F = (6.67 × 10⁻¹¹ × 15 × 15)/3²
F = 1.67 x 10⁻⁹ N
Read more about Gravitational Force at; brainly.com/question/1602310
Velocity can be thought of as the object's speed and direction, or change in position over time<span>.
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