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3 years ago

Suppose x is a normal random variable with μ = 35 and σ = 10. find p(55.5 < x < 69.7).

Mathematics

2 answers:

tangare [24]3 years ago

5 0

Answer:

$\boxed{\boxed{P(55.5 < X< 69.7)=0.01992}}$

Step-by-step explanation:

We know that,

$Z=\dfrac{X-\mu}{\sigma}$

where,

Z = z-score,

X = raw score,

μ = mean,

σ = standard deviation.

So,

$=P(55.5 < X< 69.7)$

$=P(55.5-35 < X-35< 69.7-35)$

$=P(\dfrac{55.5-35}{10}< \dfrac{X-35}{10}< \dfrac{69.7-35}{10})$

$=P(\dfrac{55.5-35}{10}< Z< \dfrac{69.7-35}{10})$

$=P(2.05< Z$

$=P(Z$

$=0.99974-0.97982\\\\=0.01992$

siniylev [52]3 years ago

4 0

The probability of $P\left({55.5$ is $\boxed{0.01992}$ .

Further Explanation:

The Z score of the standard normal distribution can be obtained as,

${\text{Z}}=\frac{{X-\mu}}{\sigma}$

Here, Z is the standard normal value, $\mu$ represents the mean, $\sigma$ represents the standard deviation.

Given:

The mean of test is $\mu =35$ .

The standard deviation of the waiting time is $\sigma=10$ .

Explanation:

The probability of mean lies between 55.5 to 69.7 can be calculated as follows,

$\begin{aligned}{\text{Probability}}&=P\left({55.5$

Further solve the above equation to obtain the probability.

$\begin{aligned}{\text{Probability}}&=\left({\frac{{55.5-35}}{{10}}$

The probability of $P\left({Z$ .

The probability $P\left({Z$ .

The probability can be calculated as follows.

$\begin{aligned}{\text{Probability}}&=P\left({Z$

Hence, the probability of $P\left({55.5$ is $\boxed{0.01992}$ .

Learn more:

1. Learn more about normal distribution brainly.com/question/12698949

2. Learn more about standard normal distribution brainly.com/question/13006989

3. Learn more about confidence interval of mean brainly.com/question/12986589

Answer details:

Grade: College

Subject: Statistics

Chapter: Confidence Interval

Keywords: Z-score, Z-value, binomial distribution, standard normal distribution, standard deviation, test, measure, probability, low score, mean, repeating, indicated, normal distribution, percentile, percentage, proportion, empirical rule.

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