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Anon25 [30]
3 years ago
9

Find the following probabilities for the standard normal random variable z: a. P(−1.36 ≤ z ≤ 1.38)= ________ b. P(−2.27 ≤ z ≤ 1.

64)= ________ c. P(z ≤ 1.33)=________ d. P(z > −0.68)=_____
Mathematics
2 answers:
Nesterboy [21]3 years ago
6 0

Answer:

a) 0.8293

b) 0.9379

c) 0.9082

d) 0.7517

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

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

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

a. P(−1.36 ≤ z ≤ 1.38)=

This is the pvalue of Z = 1.38 subtracted by the pvalue of Z = -1.36

Z = 1.38 has a pvalue of 0.9162

Z = -1.36 has a pvalue of 0.0869

0.9162 - 0.0869 = 0.8293

b. P(−2.27 ≤ z ≤ 1.64)

Same logic as a.

Z = 1.64 has a pvalue of 0.9495

Z = -2.27 has a pvalue of 0.0116

0.9495 - 0.0116 = 0.9379

c. P(z ≤ 1.33)=

This is the pvalue of Z = 1.33.

Z = 1.33 has a pvalue of 0.9082

d. P(z > −0.68)=

This is 1 subtracted by the pvalue of Z = -0.68. So

Z = -0.68 has a pvalue of 0.2483

1 - 0.2483 = 0.7517

Llana [10]3 years ago
3 0

Answer:

Step-by-step explanation:

a) P(−1.36 ≤ z ≤ 1.38)

For z = - 1.36,

The corresponding probability from the normal distribution table is 0.08691

For z = 1.38

The corresponding probability from the normal distribution table is 0.9162

Therefore,

P(−1.36 ≤ z ≤ 1.38)

= 0.9162 - 0.08691 = 0.82929

b) P(−2.27 ≤ z ≤ 1.64)

For z = - 2.27

The corresponding probability from the normal distribution table is

0.0116

For z = 1.64,

The corresponding probability from the normal distribution table is

0.9495

Therefore,

P(−2.27 ≤ z ≤ 1.64)

= 0.9495 - 0.0116 = 0.9379

c) P(z ≤ 1.33)

For z = 1.33

The corresponding probability from the normal distribution is 0.9082

Therefore,

P(z ≤ 1.33) = 0.9082

d) P(z > −0.68) = 1 - P(z ≤ −0.68)

For z = - 0.68

The corresponding probability from the normal distribution is 0.2482

Therefore,

P(z > −0.68) = 1 - 0.2482 = 0.7518

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Effectus [21]

The z or t score to be used is  (0.422,0.978)

How to find the critical value ?

Critical probability (p*) = 1 - (Alpha / 2), where Alpha is equal to 1 - (the confidence level / 100), is the unit statisticians use to determine the margin of error within a set of data in statistics.

The critical value for α = 0.13 is z_{c} = \frac{z_{1} - \alpha }{2}

The corresponding confidence interval is computed as shown below

CI = (X1_{1}  - X_{2}- z_{c} \sqrt{\frac{a_{1}^{2}}{n_{1} } + \frac{a_{2}^{2}}{n_{2} }}  ,  X1_{1}  - X_{2}+z_{c} \sqrt{\frac{a_{1}^{2}}{n_{1} } + \frac{a_{2}^{2}}{n_{2} }}  )

CI = (2.1 - 1.4- 1.514\sqrt{\frac{1^{2}}{37 } + \frac{0.5_{2}^{2}}{38 }}  ,  2.1  - 1.4 + 1.514 \sqrt{\frac{1^{2}}{37 } + \frac{0.5^{2}}{38 }}  )

CI = (0.422, 0.978)

0.422< mu1 - mu 2 < 0.978

To learn more about finding the critical value from the given link  

brainly.com/question/14040224

#SPJ4

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