Raj wants to take yoga classes. There are two yoga studios that have different membership plans.

The heights of students at a college are normally distributed with a mean of 175 cm and a standard deviation of 6 cm. One might

frosja888 [35]

Answer:

25

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 175cm

Standard deviation = 6 cm

Percentage of students below 163 cm

163 = 175 - 2*6

So 163 is two standard deviations below the mean.

By the Empirical rule, 95% of the heights are within 2 standard deviations of the mean. The other 100-95 = 5% are more than 2 standard deviations of the mean. Since the normal distribution is symmetric, 2.5% of them are more than 2 standard deviations below the mean(so below 163cm) and 2.5% are more than two standard deviations above the mean.

2.5% of the students have heights less than 163cm.

Out of 1000

0.025*1000 = 25

25 is the answer

8 0

2 years ago

Read 2 more answers

Thomas wants to invite Madeline to a party. He has an 80% chance of bumping into her at school. Otherwise, he’ll call her on the

Ivenika [448]

Answer:

84%

Step-by-step explanation:

The probability of Thomas bumping into her at school is 80%, so the probability of not bumping into her is 100% - 80% = 20%.

If he doesn't bump into her (20% chance), he will call her, and the probability of asking her in this case is 60%, so the final probability of asking her in this case is:

$P_1 = 20\% * 60\% = 12\%$

If he bumps into her (80% chance), the probability of asking her is 90%, so the final probability of asking her in this case is:

$P_2 = 80\% * 90\% = 72\%$

To find the probability of Thomas inviting Madeline to the party, we just have to sum the probabilities we found above:

$P = P_1 + P_2$

$P = 12\% + 72\% = 84\%$

5 0

2 years ago

Write the simplest form of a rational number 177/413

olchik [2.2K]

117 and 413 have no common denominator, so 117/413 is it's simplest form

8 0

2 years ago

Read 2 more answers

Which statements are true of the graph of h(x) = RootIndex 3 StartRoot x minus 4 EndRoot? Check all that apply. The domain of h(

Nastasia [14]

True statements:

The domain of h(x) is the set of all real numbers.

The range of h(x) is the set of all real numbers

Step-by-step explanation:

The function given in this problem is

$h(x)=\sqrt[3]{x-4}$

Now let's analyze the statements given:

- The domain of h(x) is the set of all real numbers. --> TRUE. The domain of a function is the set of values allowed for x. Here there is no restriction for the value of x, since the argument of an odd root can have any value (either positive or negative), so the domain of h(x) is the set of all real numbers.

- The range of h(x) is the set of all real numbers. --> TRUE. The range of a function is the set of values that the y can take. In this case, y can take any value: in fact, as $x \rightarrow +\infty$ , then $y \rightarrow +\infty$ , and as $x \rightarrow -\infty$ , then $y \rightarrow -\infty$ , and since there are no points of discontinuity in the function, this means that it can take any value of y.

For all points (x, h(x)), h(x) exists if and only if x – 4 > 0 --> FALSE. As we stated in part 1), the argument of a cubic root can be either positive or negative, so the function is defined also for x - 4 < 0.

The graph of h(x) is a translation of f(x) down 4 units. --> FALSE. The form of f(x) is not given so we can't evaluate this statement.

The graph of h(x) intercepts the x-axis at (4, 0). --> FALSE. In fact, when $x=0$ , the value of the function is