When it comes to determining the probability of a range within a nonstandard normal distribution, it requires an assessment of the area under the curve within the specified range. This is achieved by standardizing the distribution, which entails subtracting the mean and dividing by the standard deviation. Following this, one can utilize Z-tables or appropriate software to ascertain the corresponding probabilities.
| Topic | Problem | Solution |
|---|---|---|
| None | In a survey of a group of men, the heights in the… | The problem is asking for the probability of a study participant having a height less than 67 inche… |
| None | The weight of an organ in adult males has a bell-… | The empirical rule, also known as the 68-95-99.7 rule, states that for a normal distribution, almos… |
| None | Question 9 of 11 , Step 1 of 1 $9 / 15$ Correct 0… | The empirical rule, also known as the 68-95-99.7 rule, states that for a normal distribution, almos… |
| None | Find the area of the shaded region. The graph to … | The question is asking for the area under the curve of a normal distribution, which is equivalent t… |
| None | The weights for newborn babies is approximately n… | Given that the weights for newborn babies is approximately normally distributed with a mean of 5.7 … |
| None | A variable is normally distributed with mean 20 a… | The problem is asking for the area under the curve of a normal distribution. This is equivalent to … |
| None | A set of exam scores is normally distributed with… | Given that the set of exam scores is normally distributed with a mean of 84 and a standard deviatio… |
| None | When women were finally allowed to become pilots … | The problem is asking for the probability that the mean weight of 35 randomly selected women is bet… |
| None | Assume that females have pulse rates that are nor… | We are given that the mean pulse rate of females is \(\mu = 73.0\) beats per minute and the standar… |
| None | If $n p \geq 5$ and $n q \geq 5$, estimate $P($ f… | The problem is asking to estimate the probability of getting fewer than 5 successes in a binomial d… |
| None | Assume that females have pulse rates that are nor… | Given that the pulse rates of females are normally distributed with a mean of \(\mu = 72.0\) beats … |
| None | A survey found that women's heights are normally … | Given that the mean height of men is 67.3 inches with a standard deviation of 3.3 inches, we need t… |
| None | A survey found that women's heights are normally … | Given that the mean height for men is 67.3 inches with a standard deviation of 3.3 inches, we need … |
| None | Assume that military aircraft use ejection seats … | We are given that women's weights are normally distributed with a mean of \(161.8 \mathrm{lb}\) and… |
| None | A survey found that women's heights are normally … | Given that women's heights are normally distributed with a mean of 63.4 inches and a standard devia… |
| None | A survey found that women's heights are normally … | Given that women's heights are normally distributed with a mean of 63.4 inches and a standard devia… |
| None | For a certain type of light, the number of hours … | We are given a problem of normal distribution. The mean (\(\mu\)) is 5000 hours and the standard de… |
| None | 1. A manufacturer is producing metal rods, whose … | Given that the lengths of the metal rods are normally distributed with a mean of \(75.0 \mathrm{~cm… |
| None | The annual salary for one particular occupation i… | The problem provides us with the following information: the mean annual salary for a particular occ… |
| None | Suppose that the walking step lengths of adult ma… | We are given that the mean (\(\mu\)) of the step lengths of adult males is 2.6 feet and the standar… |
| None | A population of values has a normal distribution … | Given a population of values with a normal distribution, where the mean \(\mu\) is 123.5 and the st… |
| None | A manufacturer knows that their items have a leng… | We are given that the lengths of the items are normally distributed with a mean of 17.4 inches and … |
| None | Suppose the age that children learn to walk is no… | Given that the age that children learn to walk is normally distributed with a mean (\(\mu\)) of 12 … |
| None | In a survey of a group of men, the heights in the… | The problem is asking for the probability that a study participant has a height that is more than 7… |
| None | work Chapter 6 Question 48, 6.6.8-T , HW Score: $… | The problem is asking to estimate the probability of getting at least 7 successes in a binomial dis… |
| None | work Chapter 6 Question 50, 6.6.11-T , HW Score: … | The problem is asking for the probability that exactly 32 out of 121 eligible voters voted, given t… |
| None | The average price of a college math textbook is $… | The distribution of x is given as a normal distribution with a mean of $177 and a standard deviatio… |
| None | The manager of a computer retails store is concer… | The replacement times for the model laptop of concern, represented by X, are normally distributed w… |
| None | If the mean serum cholesterol level is 225 and th… | Given that the mean serum cholesterol level is 225 and the standard deviation is 22, we are asked t… |
| None | Assume that adults have IQ scores that are normal… | Given that adults have IQ scores that are normally distributed with a mean of \(\mu=105\) and a sta… |
| None | In a survey of a group of men, the heights in the… | We are given that the heights are normally distributed with a mean of 68.1 inches and a standard de… |
| None | Assume the random variable $x$ is normally distri… | We are given a normally distributed random variable $x$ with mean $\mu=50$ and standard deviation $… |
| None | Suppose that the distance of fly balls hit to the… | Let's denote the distance of fly balls hit to the outfield as \(X\). The distribution of \(X\) is n… |
| None | The amount of syrup that people put on their panc… | Given that the amount of syrup that people put on their pancakes is normally distributed with a mea… |
| None | Question 3 (3 marks) Quality checks are regularly… | Calculate the z-scores for 20.2 hours and 22 hours using the formula: \(z = \frac{x - \text{mean}}{… |
| None | 5 For a normal distribution, $P(X \leq 23.8)=91.9… | Given probabilities: $P(X \leq 23.8) = 91.92%$ and $P(X \leq 17.15) = 30.85%$ |
| None | 2. The stopping distance of a certain car traveli… | Calculate the z-scores for 120 and 140 feet: \(z_1 = \frac{120 - 130}{5}\) and \(z_2 = \frac{140 - … |
| None | When Evelyn runs the 400 meter dash, her finishin… | Step 1: Find the z-scores for 71 and 76 seconds |
| None | IQ scores are normally distributed with a mean of… | 1. Calculate the z-scores for 106 and 125: \[ z_1 = \frac{106 - 100}{15} \approx 0.4 \] \[ z_2 = \f… |
| None | When Salma runs the 400 meter dash, her finishing… | Find the z-score for 71 seconds: \( z = \frac{x - \mu}{\sigma} = \frac{71 - 70}{0.5} \) |
| None | When Ella commutes to work, the amount of time it… | \( P(28 < X < 38) = \Phi\left(\frac{38 - 34}{4.5}\right) - \Phi\left(\frac{28 - 34}{4.5}\right) \) |
| None | - Suppose \( X \) is normal with mean 8.0 and sta… | \(Z = \frac{X - \mu}{\sigma}\) |
| None | The average amount of money spent for lunch per p… | a. \( X \sim N(6.26, 2.35^2) \) |